Question

Given a right angled triangle ABC right angled at c in which tan A = root3,tan B = 1/root3 ,show that sin A. Cos B-Cos A. Sin B = 1/2.

Answer 1

Tan A = root 3 =tan 60°
A = 60°
Similarly, tan B = 1/root3=tan 30°
B =30°

Substituting values of A&B,
Sin 60. Cos 30 - sin 30.cos60
root 3/2. Root3/2 - 1/2.1/2
On solving we get,
3/4-1/4
=2/4=1/2