Question

if cosA=sin(2A-18), find A​

Answer 1

Answer:

a= 32 is the answer of the question

Answer 2

Solution:-

Given,

cosA = sin(2A - 18)

Here we are going to use the concept of allied angles

We know that sin(90 - A) = cosA

Using the above formula,

$\to$ sin(90 - A) = sin(2A - 18)

Therefore,

$\to$ 90 - A = 2A - 18

Rearranging terms

$\to$ 90 + 18 = 2A + A

$\to$108 = 3A

$\to$ A = $\rm 36^{\circ}$

Check:-

RHS:-

$\to$ sin(2x36 - 18)

$\to$ sin(72 - 18)

$\to$ sin54

Using the formula sin(90 - A) = cosA

Therefore,

$\to$ We can write sin54 as cos(90 - 54) = cos36

LHS:-

cos36 = RHS

Hence,

$\boxed{\rm \red{ A = 36^{\circ}}}$