Question

Find θ if 0° < θ ≤ 90°.

2 sin² θ + cos² 45° = tan² 45°

Answer 1

Given:

0° < θ ≤ 90°

2 sin² θ + cos² 45° = tan² 45°

Step 1: Use standard trigonometric values

cos 45° = `1/sqrt2 →  cos^2 45° = 1/2`

tan 45° = 1 → tan² 45° = 1

`2 sin^2 θ + 1/2 = 1`

Step 2:

`2 sin^2 θ = 1 − 1/2 = 1/2`

`sin^2 θ = 1/4 → sin θ = 1/2`   ...[Since 0° < θ ≤ 90°]

θ = `1/2`

θ = 30°