Verify the identites

Question

^{sec2x= 1/}1-2sin²x

Answer 1

secX=1/cosX secX=hypotenuse/adjacent cosX=adjacent/hypotenuse

sec2X=1/cos2X cos2X=1-2sin²X double angle formula

cos2X=cos²X-sin²X, double angle formula, and sin²X+cos²X=1 so cos²X=1-sin²X

cos2X=1-sin²X-sin²X=1-2sin²X substitute into sec2X=1/cos2X

sec2X=1/cos2X=1/(1-2sin²X)

Answer 2

Start with cos2x = 1-2sin²x

So,

sec2x = 1/cos2x = 1/(1-2sin²x)

This is the property of the cosine/sine double angle formulas