Question

if cotA=9/12 then find sinA+cosA/sinA-cosA+secA+cosecA/secA-cosecA​

Answer 1

Given:

• $\cot( \alpha ) = \frac{9}{12}$

To Find:

• $\frac{ \sin( \alpha ) + \cos( \alpha ) }{ \sin( \alpha ) - \cos( \alpha ) } + \frac{ \sec( \alpha ) + \csc( \alpha ) }{ \sec( \alpha ) + \csc( \alpha ) }$

SoluTion:

Let, Alpha be A

WKT

$\cot( \alpha ) = \frac{ \cos( \alpha ) }{ \sin( \alpha ) } = \frac{9}{12}$

So,

$\bold{\cos( \alpha ) = 9 \: and \: \sin( \alpha ) = 12}$

$→\;\Large{\sf{\frac{12+9}{12-9} + \frac{{\frac{1}{cos\;\alpha}}+{\frac{1}{sin\;\alpha}}}{{\frac{1}{cos\;\alpha}}-{\frac{1}{sin\;\alpha}}}}}$

AnSweR:

$\frac{ \sin( \alpha ) + \cos( \alpha ) }{ \sin( \alpha ) - \cos( \alpha ) } + \frac{ \sec( \alpha ) + \csc( \alpha ) }{ \sec( \alpha ) + \csc( \alpha ) }$ ◕➜ $\Large{\red{\mathfrak{14}}}$

Hope It Helps You ✌️