Question

Find the value of:

tan² 60° cosec² 45° + sec² 60° sin 30°

Answer 1

Given:

tan² 60° cosec² 45° + sec² 60° sin 30°

Step 1: Recall standard values

tan 60° = `sqrt3 → tan^2 60° = 3`

cosec 45° = `1/(sin 45°) = sqrt2 → "cosec"^2 45° = 2`

`sec 60° = 1/(cos 60°) = 2 → sec^2 60° = 4`

sin 30° = `1/2`

Step 2: Calculate each part

tan² 60° ⋅ cosec² 45° = 3 ⋅ 2 = 6

sec² 60° ⋅ sin 30° = 4 ⋅ `1/2` = 2

= 6 + 2   ...[Adding]

= 8