Question

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)

Answer 1

see the attached picture for the answer:

Answer 2

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.