cos2x = 2-sec^2x/sec^2x

Question

identity problem.

Answer 1

[We know that Cos2x = Cos^2x - Sin^2x

Cos2x  = Cos^2x - (1-Cos^2x)

Cos2x  = 2Cos^2x - 1]

Right hand side identity

= (2-Sec^2x)/Sec^2x

= 2/Sec^2x - Sec^2x/Sec^2x

= 2/Sec^2x - 1

= 2Cos^2x -1

= Cos2x

= Left hand side identity.