Question

if secant theta + tan theta equal to P find the value of cosec and theta
$\sqrt{8}$

Answer 1

$\huge{ \boxed{HEYA}}$

$\sec( \theta) + \tan( \theta) = p$
$sec( \theta) - \tan( \theta) = \frac{1}{p}$
$2 \sec( \theta) = p + \frac{1}{p}$
$\sec( \theta) = \frac{p {}^{2} + 1}{2p}$
$\cos( \theta) = \frac{1}{ \sec( \theta) }$
$\cos( \theta) = \frac{2p}{p {}^{2} + 1 }$

similarly,
$\tan( \theta) = \frac{p {}^{2} - 1 }{2p}$

$\sin( \theta) = \tan( \theta) \times \cos( \theta)$
$\sin( \theta) = \frac{2p}{p {}^{2} + 1 } \times \frac{p {}^{2} - 1}{2p}$
$\sin( \theta) = \frac{p {}^{2} - 1 }{p {}^{2} + 1}$
so,
$\csc( \theta) = \frac{p {}^{2} + 1 }{p {}^{2} - 1 }$

$\huge{ \boxed{thanks}}$