Question

Without using trigonometric tables, prove that:

tan²56° – cot²34° = 0

Answer 1

Given: Let the angles 56° and 34° be as stated.

To Prove: tan²56° – cot²34° = 0

Proof [Step-wise]:

1. Note that 56° + 34° = 90°.

2. Use the complementary-angle identity cot θ = tan(90° – θ).

3. Apply the identity with θ = 34°:

cot 34° = tan(90° – 34°)

= tan 56°

4. Square both sides: cot²34° = tan²56°.

5. Rearranging gives: tan²56° – cot²34°

= tan²56° – tan²56°

= 0

tan²56° – cot²34° = 0, as required.