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

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15-03-2017
Mathematics

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

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LammettHash LammettHash · Answer 1 · 2017-03-15T17:41:28+01:00

LammettHash LammettHash

15-03-2017

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

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