prove that :

LHS

= 3 sin 30° sec 60° - 4 sin 150° cot 45°

= 3 sin 30° sec 60° - 4 sin (90° × 1 + 60°)cot 45°

We know that when n is odd, sin → cos.

= 3 sin 30° sec 60° - 4 cos 60° cot 45°

= 3 (1/2) (2) – 4 (1/2) (1)

= 3 – 2

= 1

= RHS

Hence proved.