Question

prove that

Cos(x)/sin(x)= 2cos^2(x)/sin(2x)

Answer 1

from L. H. S.

=
$\frac{ \cos(x) }{ \sin(x) } = \frac{2 \cos(x) \times \cos(x) }{2 \sin(x) \times \cos(x) } \\ \\ but \: \: 2 \sin( \alpha ) \times \cos( \alpha ) = \sin(2 \alpha ) \\ \\ therefore \\ \\ \frac{2 \cos(x) \times \cos(x) }{2 \sin(x) \times \cos(x) } \\ \\ = \frac{ 2\cos {}^{2} (x) }{ \sin(2x) }$
=R. H. S.

proved

hope it helps....