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.