Question

Express cot 78° + sec 64° in terms of trigonometric ratios of angles between 0° and 45°.

Answer 1

Given: cot 78° + sec 64°.

Step-wise calculation:

1. Use complementary-angle identities: 

cot θ = tan (90° – θ) and sec θ = cosec (90° – θ)

2. cot 78° = tan (90° – 78°) 

= tan 12°

3. sec 64° = cosec (90° – 64°) 

= cosec 26°

cot 78° + sec 64° = tan 12° + cosec 26°.