Can someone help me with this trig identity?

Question

sec^2x=(sec 2x)(2-sec^2x)

Answer 1

Prove the identity. I assume you mean:

sec²x = (sec 2x)(2 - sec²x)
__________

Right Hand Side = (sec 2x)(2 - sec²x)

= [1/(cos 2x)](2 - 1/cos²x)

= [1/(2cos²x - 1)][(2cos²x - 1)/cos²x]

= 1/cos²x = sec²x = Left Hand Side