Question

Prove-
sin(60-theta) = cos(30+theta)​

Answer 1

Let theta be equal to x.

sin ( 60°+x)

= sin 60.cos x + cos 60.sinx

=[(√3 cos x) /2 + (1 sin x) /2]

cos (30 - x)

= cos 30.cos x + sin 30.sin x

=[ (√3 cos x) /2 + (1 sin x) /2]

Therefore, sin ( 60 + x) - cos ( 30 - x)

= [(√3 cos x) /2 + (1 sin x) /2] - [(√3 cos x) /2 + (1 sin x) /2]

= 0

The answer is 0