Question

If 2θ + 45° and 30° − θ are acute angles, find the degree measure of θ satisfying sin (2θ + 45°) = cos (30° − θ).

Answer 1

SOLUTION :  

Given : (2θ + 45°) & (30° + θ) and  sin(2θ + 45°) = cos(30° + θ )

sin(2θ + 45°) = cos(30° + θ )

sin(2θ + 45°) = sin(90° −(30°−θ))

[sin(90° −θ ) = cos θ]

sin(2θ + 45°) = sin(90° − 30° + θ)

On equating both sides,

(2θ + 45°) = (60° + θ )

2θ - θ  = 60° - 45°

θ = 15°  

Hence, the degree measure of θ = 15°.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Here I am using A instead of theta.

Given (2A + 45) and (30 - A) are acute

angles.

*********************************

We know that ,

sin( 90 - A ) = cosA

*********************************

sin ( 2A + 45° ) = cos ( 30° - A )

=> sin( 2A + 45° ) = sin[ 90°-(30°-A)]

=> sin(2A+45°) = sin( 90° - 30° + A )

=> sin( 2A + 45° ) = sin ( 60° + A )

=> 2A + 45° = 60° + A

=> 2A - A = 60° - 45°

=> A = 15°

•••••