Question

Express the following in terms of trigonometric ratios of angles between 0° and 45°.

sin 72° + cosec 72°

Answer 1

Given: sin 72° + cosec 72°

Step-wise calculation:

1. Write 72° as 90° – 18°, so sin 72° + cosec 72° = sin(90° – 18°) + cosec(90° – 18°).

2. Use complementary identities sin(90° – θ) = cos θ and cosec(90° – θ) = sec θ to get sin(90° – 18°) + cosec(90° – 18°) = cos 18° + sec 18°.

sin 72° + cosec 72° = cos 18° + sec 18°, where 18° lies between 0° and 45°.