Question

Without using trigonometric tables, prove that:

sin²12° + sin²78° = 1

Answer 1

Given: sin²12° + sin²78°

To Prove: sin²12° + sin²78° = 1

Proof [Step-wise]:

1. Note that 78° = 90° – 12°

So, sin 78° = sin (90° – 12°)

= cos 12°

2. Substitute: sin²12° + sin²78° = sin²12° + cos²12°.

3. Use the Pythagorean identity sin²θ + cos²θ = 1 to get sin²12° + cos²12° = 1.