Question

if sec tita plus tan tita is equal to p find the value of cosectita

Answer 1

sec tita+ tan tita = p
1/cos tita + sin/cos tita =p
1+sin tita/ cos tita=p
1+ sin tita = p cos tita
sin tita=pvos tita -1
1/sin=cosec
so, cosec tita= 1/(p cos tita -1)

Answer 2

Let (theta) be (alpha).
$\: \: \: \: \: \: \: \sec( \alpha ) + \tan( \alpha ) = p \\ = > \frac{1}{ \cos( \alpha ) } + \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = p \\ = > \frac{1 + \sin( \alpha ) }{ \cos( \alpha ) } = p \\ = > 1 + \sin( \alpha ) = p \cos( \alpha ) \\ = > \sin( \alpha ) = p \cos ( \alpha )-1 \\ \\ = > \csc( \alpha ) = \frac{1}{ \sin( \alpha ) } \\ = > \csc( \alpha ) = \frac{1}{p \cos( \alpha )-1 }.$

Above,
csc means cosec.

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