Question

Prove that cos (60 + x).cos(60-x) - sin(60 + x) sin(60-x) = -1/2

Answer 1

Solution :

Let A = 60 + x ,

B = 60 - x ,

A + B = 60+x+60-x = 120

Now ,

LHS = cosA cosB - sinAsinB

= Cos ( A + B )

= Cos 120°

= Cos ( 90 + 30° )

= - sin 30°

= -1/2

= RHS

••••

Answer 2

Let A = 60 + x ,

B = 60 - x ,

A + B = 60+x+60-x = 120

Now ,

LHS = cos A cos B - sin A sin B

= Cos ( A + B )

= Cos 120°

= Cos ( 90 + 30° )

= - sin 30°

= -1/2

= RHS