Question

if sec theta +tan theta=p, then find the value of sin theta , tan theta , sec they in terms of p.

Answer 1

hope the answer helps

Answer 2

Answer:

$tan\Theta$ = $\frac{p^2 - 1}{2p}$

$sin\Theta$ = $\frac{p^2 - 1}{p^2 + 1}$

Step-by-step explanation:

According to this question

$sec\Theta + tan\Theta$ = p

We know that, $sec^2\Theta$ = $1+ tan^2\Theta$

                        $sec\Theta$ = $\sqrt(1+ tan^2\Theta)$

So, $\sqrt(1 + tan^2\Theta) + tan\Theta$ = p

$\sqrt(1 + tan^2\Theta)$ = $p - tan\Theta$

Square both side,

$1 + tan^2\Theta$ = $(p - tan\Theta)^2$

$1 + tan^2\Theta$ = $p^2 - tan^2\Theta - 2ptan\Theta$

1 = $p^2 - 2p\times tan\Theta$

$2p\times tan\Theta$ = $p^2 - 1$

$tan\Theta$ = $\frac{p^2 - 1}{2p}$

Then,

$sin\Theta$ = $\frac{p^2 - 1}{p^2 + 1}$