Question

Prove me that cosA + sinA by cosA - sinA = 1 + tanA by 1 - tanA​

Answer 1

★ To ProVe :-

• $\sf\frac{cos A+ sin A}{cos A - sin A} = \frac{1+tan A}{1 - tan A}$

★ As wE kNow ThaT :-

• $\large\sf\red{ \frac{sinA}{cosA} =tanA }$

★ ProOf :-

$\large\sf Taking \: L.H.S. = \frac{cos A+ sin A}{cos A - sin A}$

On dividing both the numerator and the denominator by cosA. We get,

$\sf \: L.H.S. = \frac{ \frac{ cos A+ sin A}{cosA} }{ \frac{cos A - sin A}{cosA }}$

$\sf \: L.H.S. = \frac{ \frac{ cos A}{cosA} + \frac{sin A}{cos A} }{ \frac{cos A }{cosA } - \frac{ sin A}{cos A } }$

$\sf \: L.H.S. = \frac{ 1+ {tan A} }{ 1- tan A }$

$\sf \: L.H.S. =R.H.S.$

Hence, Proved!!