Verify the following identity

(cos2x+2sin(^2)x)/(cosx)=secx

cos2x=cos^2x-sin^2x



numerator

cos^2x-sin^2x+2(1-cos^2x)

cos^2x-sin^2x+2-2cos^2x

-cos^2x-sin^2x+2

-1+2=1


denominator: cosx


numerator/deonominator


1/cosx=secx.

[(cos²x – sin²x) + 2sin²x]/cosx = (cos²x + sin²x)/cosx = 1/cosx = secx