Question

if cos2A=sin(A-15), find A

Answer 1

cos 2A = sin (A - 15) 

cos 2A = cos ( 90 - (A - 15) ) 

2A = 90 - A + 15 

3A = 105 

A = 35

Answer 2

Answer:

The value of A =  35

Step-by-step explanation:

Given

cos 2A = sin(A - 15)

Recall the concept

Complementary angles are angles whose sum is 90degrees

From the trigonometric identities of  complement angles we get

sin(90 - $\theta$) =  cos $\theta$

Solution

Given, cos 2A = sin(A - 15)

We know

The complementary angle of 2A = 90 - 2A

Hence, we have

cos 2A = sin(90-2A)

substituting in the given equation we get

Sin(90-2A) = sin(A -15)

Comparing we get

90-2A = A -15

3A = 90+15

3A = 105

A = $\frac{105}{3}$ = 35

The value of A =  35

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