How do you simplify 1/csc^2 x + (1/tan x)(cot x) + cos^2 x?

Jul 20, 2015

Given Expression = $\frac{1}{\csc} ^ 2 x + \cot \frac{x}{\tan} x + {\cos}^{2} X$

= ${\sin}^{2} x$ + ${\cos}^{2} x$ + ${\cot}^{2} x$
= 1 + ${\cot}^{2} x$
= ${\csc}^{2} x$

Explanation:

Note : I have used the formulae: ${\sin}^{2} x + {\cos}^{2} x$ = 1,
1/ tan x = cot x
and $1 + {\cot}^{2} x$ = ${\csc}^{2} x$, in the process of simplification.