Question

if sec theta+ tan theta=x, find tan theta​

Answer 1

Answer:

$\frac{ {x}^{2} - 1}{2x}$

Step-by-step explanation:

Moving sec to RHS and then squaring, we get:

$\tan^{2} ( \alpha ) = {x}^{2} + \sec ^{2} ( \alpha ) - 2x \sec( \alpha )$

Then using sec²x = 1 + tan2x and then simplifying, we get:

$\tan( \alpha ) = \frac{ {x}^{2} - 1 }{2x}$