Question

Could someone please answer and explain the following question?

Answer 1

see explanation

Explanation:

the error in the question is that

sec²x =
`(1)/(cos^2x)` ≠
`(1)/(sin^2x)` , and

csc²x =
`(1)/(sin^2x)` ≠
`(1)/(cos^2x)`

have been used incorrectly in simplifying the expression

then

`(tan^2x+1)/(1+cot^2x)`

=
`(sec^2x)/(csc^2x)`

=
`((1)/(cos^2x) )/((1)/(sin^2x) )`

=
`(1)/(cos^2x)` ×
`(sin^2x)/(1)`

=
`(sin^2x)/(cos^2x)`

= tan²x