Prove the identity using the sum to product formuals cos4xco

Prove the identity using the sum to product formuals:

cos4x-cos2x/sin2x-sin4x=tan3x

Solution

cos4x-cos2x/sin2x-sin4x = tan3x

LHS (cos4x-cos2x)/(sin2x-sin4x)

use identities : cosA - cosB = -2sin[(A+B)/2]sin[(A -B)/2]

sinA - sinB = 2sin[(A -B)/2]cos[(A +B)/2]

(cos4x-cos2x)/(sin2x-sin4x)

= (-2sin(3x)sin(x) / -2sinxcos3x

= tan3x

= RHS