Question

Express the following in terms of trigonometric ratios of angles between 0° and 45°.

sin 67° + cos 75°

Answer 1

Given: sin 67° + cos 75°

Step-wise calculation:

1. Use co-function identities: sin θ = cos(90° – θ) and cos θ = sin(90° – θ).

2. sin 67° = cos(90° – 67°) = cos 23°.

3. cos 75° = sin(90° – 75°) = sin 15°.

4. Therefore sin 67° + cos 75° = cos 23° + sin 15°.

sin 67° + cos 75° = cos 23° + sin 15°, where 23° and 15° lie between 0° and 45°.