Answer:
see explanation
Step-by-step explanation:
the error in the question is that
sec²x = [tex]\frac{1}{cos^2x}[/tex] ≠ [tex]\frac{1}{sin^2x}[/tex] , and
csc²x = [tex]\frac{1}{sin^2x}[/tex] ≠ [tex]\frac{1}{cos^2x}[/tex]
have been used incorrectly in simplifying the expression
then
[tex]\frac{tan^2x+1}{1+cot^2x}[/tex]
= [tex]\frac{sec^2x}{csc^2x}[/tex]
= [tex]\frac{\frac{1}{cos^2x} }{\frac{1}{sin^2x} }[/tex]
= [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{sin^2x}{1}[/tex]
= [tex]\frac{sin^2x}{cos^2x}[/tex]
= tan²x
