Question

Solve:$\sqrt{\sec x-1}=\tan x$

Answer 1

$\sqrt{\sec x-1}=\tan x$

$\sec x-1={\tan }^{2}x$

$\sec x={\tan }^{2}x+1$

$\sec x={\sec }^{2}x$

${\sec }^{2}x-\sec x=0$

$\sec x(\sec x-1)=0$

When,

$\sec x=0$

$\sec x\ne 0$

Not exist

When,

$\sec x-1=0$

$\sec x=1$

$\sec x=\sec 0$

$x=0$

Hence,this is the answer.

Consider the given equation,