Question

If sec A = cosec B, prove that A + B = 90°.

Answer 1

Given: sec A = cosec B.

To Prove: A + B = 90°.

Proof [Step-wise]:

1. sec A = cosec B

⇒ `1/(cos A) = 1/(sin B)`

2. Hence, cos A = sin B.

3. But sin B = cos (90° – B).

4. Therefore, cos A = cos (90° – B).

5. For acute angles, equality of cosine implies A = 90° – B.

6. Rearranging gives A + B = 90°.