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

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Answer 1 · 2015-07-20T03:44:58

Given Expression = $1/csc ^ 2 x + cot x / tan x + cos ^2 X$

= $sin ^ 2 x$ + $cos ^ 2 x$ + $cot ^ 2 x$
= 1 + $cot ^2 x$
= $csc ^ 2 x$

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.

How do you simplify 1/csc^2 x + (1/tan x)(cot x) + cos^2 x1/csc^2 x + (1/tan x)(cot x) + cos^2 x?