(B + A) + (B - A) (B - A) + (B + A) = - Vidyadip

MCQ

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

A
$\frac{{\cos B + \sin B}}{{\cos B - \sin B}}$
✓
$\frac{{\cos A + \sin A}}{{\cos A - \sin A}}$
C
$\frac{{\cos A - \sin A}}{{\cos A + \sin A}}$
D
None of these

✓

Answer

Correct option: B.

$\frac{{\cos A + \sin A}}{{\cos A - \sin A}}$

b
(b) $\frac{{\sin \,(B + A) + \cos \,(B - A)}}{{\sin \,(B - A) + \cos \,(B + A)}}$

$ = \frac{{\sin \,(B + A) + \sin \,({{90}^o} - \overline {B - A} )}}{{\sin \,(B - A) + \sin \,({{90}^o} - \overline {A + B} )}}$

$ = \,\frac{{2\,\sin \,(A + {{45}^o})\,\cos \,({{45}^o} - B)}}{{2\,\sin \,({{45}^o} - A)\,\cos \,({{45}^o} - B)}}$

$ = \frac{{\sin \,(A + {{45}^o})}}{{\sin \,({{45}^o} - A)}} $

$= \frac{{\cos A + \sin A}}{{\cos A - \sin A}}$.

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