Precalculus: Show the steps to Verify the Identity

Question

(sin2θ - cos2θ +1)/(1-cos^2θ) +1 = (2cscθ + 3secθ)/(secθ)

Answer 1

reduce left and right sides to 2cotx +3

generally convert all terms to sines and cosines, if you dont' see a more simple reduction

right side:

2cscx/secx + 3secx/secx

2cotx +3

left side

(sin2x -cos2x +1)/(1-cos^2(x)

sin2x/(1-cos^2(x) +2(1-cos^2(x)/(1-cos^2)+1

sin2x/(1-cos^2(x) +2+1

2sinxcosx/sin^2(x) +3

2cosx/sinx +3

2cotx +3

left side = right side

2cotx +3 = 2cotx +3