Question

Could someone please answer and explain the following question?

Answer 1

Answer:

see explanation

Step-by-step explanation:

the error in the question is that

sec²x = $\frac{1}{cos^2x}$ ≠ $\frac{1}{sin^2x}$ , and

csc²x = $\frac{1}{sin^2x}$ ≠ $\frac{1}{cos^2x}$

have been used incorrectly in simplifying the expression

then

$\frac{tan^2x+1}{1+cot^2x}$

= $\frac{sec^2x}{csc^2x}$

= $\frac{\frac{1}{cos^2x} }{\frac{1}{sin^2x} }$

= $\frac{1}{cos^2x}$ × $\frac{sin^2x}{1}$

= $\frac{sin^2x}{cos^2x}$

= tan²x