Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Simplify the expression. csc^2(Pi/2-x)/1+tan^2(x)

Question

asked Jul 10, 2019 81.8k views

2 Answers

Izumi Kawashima · Answer 1 · 2019-07-15T02:46:55+0000

Answer:

The value of given expression
$(\csc^2((pi)/(2)-x) )/(1+\tan^2 x)$ is 1.

Explanation:

Consider the given expression,

$(\csc^2((pi)/(2)-x) )/(1+\tan^2 x)$

We have to simplify to the lowest possible value.

Cosider the expression,

$(\csc^2((pi)/(2)-x) )/(1+\tan^2 x)$

$1+\tan^2 x= \sec^2x$ , we get,

$\Rightarrow (\csc^2((pi)/(2)-x) )/(\sec^2x)$

$\Rightarrow ((\csc((pi)/(2)-x))^2 )/(\sec^2x)$

Also,
$\csc(90-x)=\sec x$ , we get,

$\Rightarrow (\sec^2x )/(\sec^2x)$

= 1

Thus, The value of given expression
$(\csc^2((pi)/(2)-x) )/(1+\tan^2 x)$ is 1.