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Verify the following trigonometric identity (1+tanx)^2=sec^2x+2tanx

User Goblinjuice
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1 Answer

23 votes
23 votes

Verify the equation :


(1+\tan x)^2=\sec ^2x+2\tan x

solve:


=(1+\tan x)^2

Use the formula :


(a+b)^2=a^2+b^2+2ab
\begin{gathered} =(1+\tan ^{}x)^2 \\ =1^2+(\tan x)^2+2(1)(\tan x) \\ =1+\tan ^2x+2\tan x \end{gathered}

Use the formua:


1+\tan ^2x=\sec ^2x
\begin{gathered} =1+\tan ^2x+2\tan x \\ =\sec ^2x+2\tan x \end{gathered}

User Capella
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