Verify the identity 2cos2x2sin2x cotxsecxcscxtanxSolution2c

Verify the identity: (2cos2x-2)/(sin2x) = cot(x)-sec(x)csc(x)-tan(x)

(2cos2x-2)/(sin2x) = cot(x)-sec(x)csc(x)-tan(x)

Lets take more complex side i.e. RHS:

cot(x)-sec(x)csc(x)-tan(x) = cosx/sinx - 1/cosxsinx - sinx/cosx

= ( cos^2x - 1 - sin^2x)/sinxcosx

= ( cos2x -1)/sinxcosx

multiplying numerator and denominator with 2

= 2 ( cos2x -1)/2sinxcosx

= ( 2cos2x - 2)/sin2x

= LHS