Question

Prove that cosec theta/Cot theta+tan theta=cos theta​

Answer 1

Step-by-step explanation:

$\frac{ \csc( \alpha ) }{ \cot( \alpha ) + \tan( \alpha ) }$

$= \frac{ \frac{1}{ \sin( \alpha ) } }{ \frac{ \cos( \alpha ) }{ \sin( \alpha ) } + \frac{ \sin( \alpha ) }{ \cos( \alpha ) } }$

$= \frac{ \frac{1}{ \sin( \alpha ) } \times \sin( \alpha ) \cos( \alpha ) }{( \frac{ \cos( \alpha ) }{ \sin( \alpha ) } + \frac{ \sin( \alpha ) }{ \cos( \alpha ) } ) \times \sin( \alpha ) \cos( \alpha ) }$

$= \frac{ \cos( \alpha ) }{ \cos {}^{2} ( \alpha ) + \sin {}^{2} ( \alpha ) }$

$= \frac{ \cos( \alpha ) }{1}$

$= \cos( \alpha )$

Hence Proved

Answer 2

Step-by-step explanation:

L.H.S. = cosecθ

cotθ+tanθ

1

sinθ

= cosθ+sinθ

sinθ +cosθ

1

sinθ

= sin²θ+cos²θ

sinθ.cosθ

1

sinθ

= 1

sinθ.cosθ

= 1 × sinθ.cosθ

sinθ 1

= cosθ