Question

cosecA-cotA×cosecA+cotA=1​

Answer 1

QUESTION :

cosecA-cotA×cosecA+cotA=1.

ANSWER:

We use the trigonometry identity to solve the question :

$\csc( \alpha ) = \frac{1}{ \sin( \alpha ) }$

$\cot( \alpha ) = \frac{ \cos( \alpha ) }{ \sin( \alpha ) }$

${ \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} = 1$

I LET A AS ALPHA .

so taking LHS;

$\csc( \alpha ) - \cot( \alpha ) \times \csc( \alpha ) + \cot( \alpha )$

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

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

$\frac{ {1 - \cos( \alpha ) }^{2} }{ { \sin( \alpha ) }^{2} }$

$\frac{ { \sin( \alpha ) }^{2} }{ { \sin( \alpha ) }^{2} } \\ 1$

LHS = RHS

HENCE PROVED.

PLZ MARK AS BRAINLIEST