SOLUTION: Prove that : (sec^2x + 2tanx)/(cosx + sin x)^2 = sec^2x

Question 782106: Prove that :
(sec^2x + 2tanx)/(cosx + sin x)^2 = sec^2x
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
(sec^2x + 2tanx)/(cosx + sin x)^2
(1+tan^2x+2tanx)/(cos^2x+sin^2x+2sinxcosx)

(1+tanx)^2/(1+2sinxcosx)
(1+(sinx/cosx))^2/(1+2sinxcosx)

((cosx+sinx)/cosx)^2/(1+2sinxcosx)

((cos^2x+2sinxcosx+sin^2x)/cos^2x))/(1+2sinxcosx))

((1+2sinxcosx)/cos^2x)*(1/(1+2six.cosx))

1/cos^2x)

sec^2x

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