Question

Without using trigonometric tables, prove that:

sin 32° cos 58° + cos 32° sin 58° = 1

Answer 1

Given: sin 32° cos 58° + cos 32° sin 58°

To Prove: sin 32° cos 58° + cos 32° sin 58° = 1

Proof [Step-wise]:

1. Recall the sine addition formula: sin(A + B) = sin A cos B + cos A sin B.

2. Apply the formula with A = 32° and B = 58°:

sin(32° + 58°) = sin 32° cos 58° + cos 32° sin 58°

3. Compute 32° + 58° = 90°, so the left side is sin 90°.

4. sin 90° = 1.

Therefore sin 32° cos 58° + cos 32° sin 58° = sin 90° = 1.