Question

Without using trigonometric tables, prove that:

sec²29° – cot²61° = 1

Answer 1

Given: sec²29° – cot²61°

To Prove: sec²29° – cot²61° = 1

Proof [Step-wise]:

1. Note that 61° = 90° – 29°.

2. Using the complementary-angle identity cot(90° – A) = tan A, we get 

cot 61° = cot(90° – 29°) 

= tan 29°

3. Therefore cot²61° = tan²29°.

4. Substitute into the expression:

sec²29° – cot²61° = sec²29° – tan²29°

5. Use the Pythagorean identity sec²θ = 1 + tan²θ

So, sec²29° – tan²29° = 1.

Hence, sec²29° – cot²61° = 1.