Question

sin^2 x (cot^2 x+1)

Answer 1

Use the Pythagorean Identity:

1 + cot^2(x) = csc^2 (x)

so you have (sin^2 x)(csc^2 x)

but csc^2 x = 1/sin^2(x)

so you have sin^2(x) times 1/sin^2(x) = 1