Question

if 20+45 and 30-0 are acute angles, find the degree measure of a satisfying sin [20+45]=cos[30-0]

Answer 1

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Answer 2

QUESTION :-

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

SOLUTION :-

sin(2θ + 45°) = cos(30° + θ )

⇒sin(2θ + 45°) = sin[90° −(30°−θ)]

As sin(90° −θ ) = cos θ, and vice-versa.

⇒sin(2θ + 45°) = sin(90° − 30° + θ)

⇒2θ + 45° =  90° − 30° + θ

Same bases get cancelled

⇒2θ + 45° = 60° + θ

⇒2θ - θ = 60° - 45°

⇒θ = 15°       . . . ANSWER