Prove the identity sin 3 theta cos theta sin theta cos 3 th

Prove the identity: sin 3 theta cos theta - sin theta cos 3 theta/sin 4 theta = sec 2 theta Prove the identity:

Solution

Taking left hand side

(sin3cos - sincos3)/(sin4) = sin(3-)/sin4 = sin(2)/sin2(2)

= sin2/(2sin(2)cos(2)) = 1/2cos2 = (sec2)/2

Identity should be (sin3cos - sincos3)/(sin4) = sec(2)/2

In the question given Right hand side = sec(2) that\'s not an identity.