How do you prove  cot^2 x +csc^2 x = 2csc^2 x - 1?

Dec 8, 2015

Using the identity:
${\csc}^{2} x - {\cot}^{2} x = 1$ ...............(1)

from the problem
${\cot}^{2} x + {\csc}^{2} x - 2 {\csc}^{2} x = - 1$

$\implies {\cot}^{2} x - {\csc}^{2} x = - 1$

$\implies {\csc}^{2} x - {\cot}^{2} x = 1$

which is the identity (1)