Verify this equation

Question

(csc²(x)+1)/(1+cot²(x)) = sin²(x)+1

Thanks for the help!

Answer 1

[1/sin^2 + sin^2/sin^2]/[ sin^2/sin^2 + cos^2/sin^2] =

(1 + sin^2) / sin^2 divided by (sin^2 + cos^2) / sin^2 =

(1 + sin^2)/sin^2 * sin^2/(1) <--- fraction flips; sin^2+cos^2 = 1

1+sin^2 <--- sin^2 cancels