Question

Prove that sin 600 cos 390+ cos 480 sin 150 = 1

Answer 1

We know that

sin(3π+θ)=−sin(θ)cos(2π+θ)=cos(θ)tan(4π+θ)=tan(θ)cot(3π+θ)=cot(θ)cot(π2+θ)=−tan(θ)

Now Consider

sin(600°)cos(390°)+tan(765°)cot(675°)=sin(3π+60°)cos(2π+30°)+tan(4π+45°)cot(3π+135°)=−sin(60°)cos(30°)+tan(45°)cot(135°)=−sin(60°)cos(30°)+tan(45°)cot(π2+45°)=−sin(60°)cos(30°)−tan(45°)tan(45°)=−3√2×3√2−1=−34−1=−74