Question

If sin θ = cos (θ − 45°), where θ and θ − 45° are acute angles, find the degree measure of θ.

Answer 1

SOLUTION :  

Given : sin θ = cos (θ - 45°) and (θ - 45°) are acute angles.

sin θ = cos (θ - 45°)

cos (90° - θ) = cos (θ - 45°)

[cos (90° - θ) = sin θ]

On equating both sides,

(90° - θ) =  (θ - 45°)

90° + 45° =  θ +  θ  

135° = 2θ

θ = 135°/ 2  = 67 ½°  

θ = 67 ½°  

Hence, the degree measure of θ is 67 ½°  .

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer: 62.5°

Step-by-step explanation:

Theta = A

SinA = Cos(A-45°)

Cos(90° - A) = Cos(A-45°)

By comparing the angles,

90° - A = A - 45°

2A = 135°

A = 135/2

A = 62.5°

Hope it helps...