verify cos(a+b)/cos(a) cos(b) =1-tan(a) tan(b)

Verify Cos(a+b)/cos(a) Cos(b) =1-tan(a) Tan(b)

Answers

Answer 1

The identity as been verified/proved as:

[tex]1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b[/tex]

Given that:

[tex]\frac{\cos(a + b)}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Apply cosine identity to the numerator

[tex]\frac{\cos\ a\ cos\ b - \sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Split the fraction:

[tex]\frac{\cos\ a\ cos\ b}{\cos\ a\cos b} - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Cancel out common terms

[tex]1 - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

In trigonometry, we have:

[tex]\frac{\sin \theta}{\cos \theta} = \tan \theta[/tex]

So, the equation becomes:

[tex]1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b[/tex]

Hence, the identity has been verified

Read more about trigonometry identities at:

https://brainly.com/question/21055284


Related Questions

What is the greatest common factor of 12 and 18?
A. 2 B. 6 C. 4 D. 12

Answers

Answer:

B. 6

Step-by-step explanation:

D. 12 cant be multiplied to get 18

C. 4 cant be multiplied to get 18

A. 2 is a common factor of 12 and 18 but not the greatest.

B. 6 times 2 is 12 and 6 times 3 is 18 so 6 is the greatest common factor.

Answer:

B

Step-by-step explanation:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

The common ones are 1, 2, 3, and 6. The greatest one among these is 6.

Factors are numbers you multiply with another natural number to get another number. For example, the factors of 16 will be all the numbers that can be multiplied with an integer to get 16. 1* 16 is 16, so 1 will work. 2 *8 is 16, so 2 will work. But, 3 * 16/3 is 16 so 3 won't work. You get the point. Hope this helps and pls give brainliset.

Are 3:5and 1:2 equivalent

Answers

Answer:

No. They are not equivalent.

Step-by-step explanation:

[tex]\frac{3}{5} \neq \frac{1}{2}[/tex]

=> [tex]\frac{6}{10} \neq \frac{5}{10}[/tex]

Therefore, 3/5 and 1/2 are not equivalent.

Hoped this helped.

Answer:

yes

Step-by-step explanation:

they are equivalent

PLS HELP!!!!! What are the zeros of polynomial function [tex]F(x) = x^4 - 10x^2 + 16[/tex]

Answers

Answer:

(-√8, 0), (-√2, 0), (√2, 0), (√8, 0)

Step-by-step explanation:

3x+y=5
2x-y=0
Plsss help i need step by step plsss 9th grade

Answers

Answer:

x = 1

y = 2

Step-by-step explanation:

3x + y = 5

y = 5 - 3x

-----

2x - (5 - 3x) = 0

2x + 3x - 5 = 0

5x - 5 = 0

5x = 5

x = 1

-----

3(1) + y = 5

3 + y = 5

y = 2

Step-by-step explanation:

1. you add 3x to the other side to get y=-3x+5

2. then for the other equation you subtract 2x to the other side to get -1y=2x

3.then you divide by -1 to get y=2x

y=-3x+5 and y=2x

Which expression is equal to the expression below?
(2• 6)4

Answers

Answer:

2 × 6 × 4

Step-by-step explanation:

This can also be written like this.

2x2 +5x+8
Given x 3-2, the expression
x+2.
is equivalent to

Answers

Answer:

x=-1

Step-by-step explanation:

so 3-2 is 1 right so what humber + 2 is 1 well -1 becasue -1 + 1 is 0 and plus 2 would be 1 so its -1 (or x= -1). Hope this helped!

The expression equivalent to the given expression is (2x+1)+6/(x+2)

What is an expression?

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, (2x²+5x+8)/(x+2)

From the given options,

Simplifying (2x+1)+6/(x+2), we get,

= (2x+1)(x+2)+6/(x+2

= (2x²+4x+x+6+2)/(x+2)

= (2x²+5x+8)/(x+2)

Since, we get the main expression by solving the option expression,

Hence, the expression equivalent to the given expression is (2x+1)+6/(x+2)

For more references on expressions, click;

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A dump truck is filled with 82.16 pounds of gravel. It drops off 77.29 pounds of gravel at a construction site. How much gravel is left on the truck?

Answers

Answer:

4.87lbs

Step-by-step explanation:

82.16-77.29=4.87

The product of 0.4 and a number is 8 write a mathematical expression to represent the verbal expression. Use n for the variable solve the expression

Answers

Answer:

0.4n = 8

n = 20

Step-by-step explanation:

0.4n = 8

n = 8 / 0.4

n = 20

WILL GIVE BRAINLIEST!

Answers

Answer:

425

Step-by-step explanation:

225/24 then multiply the answer by 40

Rate of change for y=5x+30

Answers

Answer:

5

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Solve the proportion. x/6 = 20/24

Answers

X/6 = 20/24

Cross multiply:

24x = 120

Divide both sides by 24

X = 5

Answer: x = 5

Sara earns a basic salary of 14250 every month with an additional 12% commission on her sales. If Sara sold items worth AED 22264 last month, what was her total pay?
a. AED 16921.68
b. AED 24935.68
c. AED 1710
d. AED 2671.68

Answers

Answer:

A

Step-by-step explanation:

Commission: 22264*0.12=2671.68

Total pay: 14250+2671.68=16921.68

The total pay of Sara after adding the commission is: Option A:  AED 16921.68

How to find the net income?

Sara's total pay consists of her basic salary plus the commission on her sales.

Basic salary = AED 14250

Commission on sales = 12% of AED 22264

Commission = 0.12 * 22264

Now, calculate the commission:

Commission = 0.12 * 22264 = AED 2671.68

Total pay = Basic salary + Commission

Total pay = 14250 + 2671.68 = AED 16921.68

So, Sara's total pay is AED 16921.68

Read more about Net Income at: https://brainly.com/question/30404567

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CAN SOMEONE HELP ME PLS?

Answers

Answer:

√13

Step-by-step explanation:

1/33 is a fraction, meaning it is rational

1.6... has a repiton, meaning it is rational

-5.43 is a integer meaning it is rational

what is solve 10<-2/3(9+12b)

Answers

Ok done. Thank to me:>

Um yeah so ignore the blue circles. I need your helpp ty <3

Answers

Answer:

where is the diagram u there is must must graphic of this or diagram

Answer:

15, 6,0, 11, 7

I'm not sure but hope it helps

Step-by-step explanation:

y=8+7

=15

y=-1+7

=6

y=-7+7

=0

y=4+7

=11

y=0+7

=7

Need help with Pre college

Answers

Answer:

check online for more information

log(3+√5) + log(3 - √5) = ?​

Answers

Given that

log (3+√5) + log (3-√5)

We know that

log ab = log a + log b

⇛log [(3+√5)(3-√5)]

This is in the form of (a+b)(a-b)

Where a = 3 and b = √5

We know that

(a+b)(a-b) = a²-b²

⇛log [(3)²-(√5)²]

⇛log(9-5)

⇛log 4

Answer :- log (3+√5) + log (3-√5) = log 4

also read similar questions: log(5) + log(3) rewrite the following in the form log(c)....

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witch of the following expression is equivalent to the logarithmic expression below. log(3)5/x^2 A)log(3) 5+2 log(3)x B)log(3) 5-2 log(3)x C)2 log(3) 5 -log(3)x...

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( 4 1 ​ + 4 5 ​ ) ^ 2 + 4 3 ​ =

Answers

PEMDAS
(41 + 45) ^ 2 + 43
(86) ^ 2 + 43
7396 + 43
7439

Answer: 7,439

Step-by-step explanation:

(86)^2 + 43

7396 + 43 = 7,439

I'm pretty sure that the other user has the same answer. (godlike74)

Find the slope of the line that passes through (28, -25) and (27, 25).

Answers

Slope is the change in Y over the change in X:

Slope = (25- -25) / (27 - 28)

Slope = 50/-1

Slope = -50

help please asappppppppp​

Answers

Answer:

First Equation: 6a-23

Second Equation: 5a-20

Step-by-step explanation:

So, I think you want me to answer part 2...

For the first equation, we can see that the denominator stays the exact same, meaning the numerator will also not change.

For the second equation, we can see the denominator changed from a-3 to 5a-15. The denominator was simply multiplied by 5. Since the denominator was multiplied by five we must multiply the numerator by five as well.

5(a-4)

5a-20

Hope this helps :)

Please help me ill put the question up for a lot of point, and i will mark as brainliest!!!

Answers

Step-by-step explanation:

(2x³y^-4)^-2 = 1/(4x⁶y^‐8) = y⁸/(4x⁶)

1/(8x⁵y^-7) = y⁷/(8x⁵)

4x^-9y⁴ = 4y⁴/x⁹

so, the whole expression is then

y⁸/(4x⁶) × y⁷/(8x⁵) × 4y⁴/x⁹

4y¹⁹/(32x²⁰) = y¹⁹/(8x²⁰)

so, D is the correct answer.

In 7 hours, Deandre reads 42 chapters of a book.
What is his rate in chapters per hour?

Answers

Answer:

6 chapters per hour

Step-by-step explanation:

[tex]\frac{42 (chapters)}{7 (hours)} =6[/tex]

Hope this helps

316=5
459=6
248=4
739=?

Answers

Answe

i think it's 9

Step-by-step explanation:

316 fỉst number is 3 +2 =5

459 first number is 4+2=6

2+2=4

7+2=9:)))

When Abrams born his parent put $2000 in account that you did 1.2% interest compounded semi annually when he turns 16 in Spain to give him the money to buy a car how much will Abrams you receive on his 16th birthday

Answers

Answer:

$2421.95

Step-by-step explanation:

To calculate the final value from compound interest, we can use the formula

A = P(1+r/n)^(nt), where A represents the final amount, P is the initial amount, r is the rate, n is the number of times compounded per time period, and t is the amount of time.

Here, P is 2000, 1.2% is the rate (to convert to a decimal, we can divide by 100 to get 0.012), n = 2 because it is compounded semi-annually, and 16 is the number of years, or t. Plugging these in, we get

2000(1+0.012/2)^(2*16) = 2421.95

Astudent built a scale model of his house using a scale in which 3 inches represents 15 feet.The height of his real house is 45 feet.What is the height of the scale model in inches?
NEED HELP ASAP

Answers

Answer:

9 inches

Step-by-step explanation:

Find the missing number in this proportion.


7 =2/4

Answers

Answer:

So in between the 2 and the / there is an 8

Step-by-step explanation:

Because 28/4=7

Evaluate the expression for the given values.
12x+5y/3z, where x + 1/2, y = 6 and z = 3

Answers

Answer:

4

Step-by-step explanation:

Substitute: [tex]\frac{\frac{12}{2} +5*6}{3*3}[/tex]

Cross out the common factor: [tex]\frac{6+5*6}{3*3}[/tex]

Calculate the product or quotient: [tex]\frac{6 +30}{3*3}[/tex]

Calculate the product or quotient: [tex]\frac{6+30}{9}[/tex]

Calculate the sum or difference: [tex]\frac{36}{9}[/tex]

Cross out the common factor: [tex]4[/tex]

Answer: [tex]4[/tex]

12* 1/2 + 5*6/3*3

6 + 30/9

6 + 10/3

6 *3/3 = 18/3

18/3 + 10/3

28/3 = 9 1/3

the answer is 9 1/3

Of the 50 students in cooking club, 30% are in 7th grade. How many actual students are in 7th grade?

Answers

Answer:

15 of them are in 7th grade

Step-by-step explanation:

Caitlin has a cookie recipe that requires 1.25 pounds of sugar how many grams of sugar does she need

Answers

Answer:

For this answer, you need to do a conversion from pounds to grams. 1 pound is equal to 453.592 or just 453.6 grams if rounding is allowed. You would need to multiply 1.25 pounds to the 453.6 grams which would equal 566.99 grams or if you are rounding then it is 567 grams.

Your final answer is 567 grams of sugar.

Fred bought a shirt that
was on sale. The original
price was $15.75, but it was
20% off. How much did
Fred save?

Answers

Answer:

Fred save about 3.15$ because is 20% off

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