Question

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

Answer 1

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}$