Question

If $2\theta +{45}^o$ and ${30}^o-\theta$ are acuter angles, find the degree measure of $\theta$satisfying

sin $(2\theta +{45}^o)$ = $({30}^o-\theta )$

Answer 1

sin (2x + 45°) = cos (30° − x)

⇒ sin (2x + 45°) = sin [90° − (30° − x)]
{as, sin (90° − θ) = cos θ}

⇒ sin (2x + 45°) = sin (90° − 30° + x)
⇒ sin (2x + 45°) = sin (60° + x)
⇒ 2x + 45° = 60° + x
⇒ 2x − x = 60° − 45°
⇒ x = 15