Question

Without using trigonometric tables, prove that:

cot 34° – tan 56° = 0

Answer 1

Given: cot 34° – tan 56°

To Prove: cot 34° – tan 56° = 0

Proof [Step-wise]:

1. Note that 34° = 90° – 56°.

2. Therefore cot 34° = cot (90° – 56°).

3. Use the complementary-angle identity cot (90° – θ) = tan θ to get cot (90° – 56°) = tan 56°.

4. Substitute: cot 34° – tan 56°

= tan 56° – tan 56° 

= 0

Hence, cot 34° – tan 56° = 0, as required.