Prove the identity sin3xsinxcosx4cosxsecxSolutionsin3xsinx c

Prove the identity:

(sin(3x))/(sin(x)cos(x))=4cos(x)-sec(x)

Solution

sin3x/sinx cos x

sin3x=3sinx -4sin³x

(3sinx -4sin³x)/(sinx cos x)

3sinx/(sinx cosx) -4sin³x/sinx cos x

3/cosx   -4(1-cos²x)/cosx

(3-4+4cos²x)/cosx= (4cos²x-1)/cosx = 4cos²x/cos x   -1/cosx

                                                         =4cosx -sec x