Question

TanA + cotA = 2cosec2A

Answer 1

Explanation:

Let's simplify the Right Handed Side

`2 \csc(2 \alpha )`

`\tan( \alpha ) + \cot( \alpha ) = (2)/( \sin(2 \alpha ) )`

`\tan( \alpha ) + \cot( \alpha ) = (2)/(2\sin( \alpha ) \cos( \alpha ) )`

`\tan( \alpha ) + \cot( \alpha ) = (1)/( \sin( \alpha ) \cos( \alpha ) )`

Now, lets consider the left handed side.

`( \sin( \alpha ) )/( \cos( \alpha ) ) + ( \cos( \alpha ) )/( \sin( \alpha ) ) = (1)/( \sin( \alpha ) \cos( \alpha ) )`

`\frac{ \sin {}^(2) ( \alpha ) + \cos {}^(2) ( \alpha ) }{ \sin( \alpha ) \cos( \alpha ) } = (1)/( \sin( \alpha ) \cos( \alpha ) )`

`(1)/( \sin( \alpha ) \cos( \alpha ) ) = (1)/( \sin( \alpha ) \cos( \alpha ) )`