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Prove the identity. (tanx+1)^2=(1+2sinxcosx)/(cos^2x)

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LammettHash

\((\tan x+1)^2=\tan^2x+2\tan x+1\)
\(=\sec^2x+2\tan x\)
\(=\dfrac1{\cos^2x}+2\dfrac{\sin x}{\cos x}\)
\(=\dfrac1{\cos^2x}+\dfrac{2\sin x\cos x}{\cos^2x}\)
\(=\dfrac{1+2\sin x\cos x}{\cos^2x}\)

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