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$\frac{{\cos A - \sin A}}{{\cos A + \sin A}}$
- DNone of these
$ = \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)}} $
$= \frac{{\cos A + \sin A}}{{\cos A - \sin A}}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$I.$ If $n$ is a composite number, then $n$ divides $(n-1) ! .$
$II$. There are infinitely many natural numbers $n$ such that $n^3+2 n^2+n$ divides $n !$