Sec^2x-1=sec2x-1/sec2x=+1

Question

verify the identity

Answer 1

left side = tan^2x = sin^2x/cos^2x

right side = (1/cos2x -1)/(1/cos2x+1)

numerator of the right side = 1/(cos2x -1) = 1/[(cos^2x - sin^2x) -1] =1/ (2-sin^2x)

denominator of the right side = 1/(cos^2x - sin^2x +1) = 1/2cos^2x

numerator over denominator = 2cos^2x/2sin^2x = cos^2x/sin^2x = tan^2x = right side

tan^2x =tan^2x

left side = right side