Question

CosA+sinA/ cosA - sinA = tan (45* +A)

Answer 1

Step-by-step explanation:

We have,

$\rm \frac{ \cos(A) + \sin(A) }{\cos(A) - \sin(A)}$

$\rm= \frac{ \frac{ \cos(A) + \sin(A)}{ \cos(A) } }{ \frac{\cos(A) - \sin(A)}{ \cos(A) }}$

$= \rm \frac{ 1 + \tan(A) }{1 - \tan(A)}$

$= \rm \frac{ \tan( \frac{\pi}{4} ) + \tan(A) }{1 - \tan( \frac{\pi}{4} ) . \tan(A)}$

$= \rm \tan \bigg( \frac{\pi}{4} + A \bigg)$

$= \rm \tan \bigg( 45 \degree + A \bigg)$