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

Sagot :

Verify the equation :

[tex](1+\tan x)^2=\sec ^2x+2\tan x[/tex]

solve:

[tex]=(1+\tan x)^2[/tex]

Use the formula :

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

Use the formua:

[tex]1+\tan ^2x=\sec ^2x[/tex][tex]\begin{gathered} =1+\tan ^2x+2\tan x \\ =\sec ^2x+2\tan x \end{gathered}[/tex]

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