sin²x (1 + cot²x) = 1

Question

sin²x (1 + cot²x) = 1

LHS: sin²x (1 + cot²x)

= sin²x (csc²x) (what rule)

= sin²x (1 / sin²x) (what rule)

= 1 (what rule)

(Algebra, Reciprocal, Quotient, Pythagorean, or Odd/Even)

Answer 1

1+cot²x = 1 + 1/tan²x (def of cotx) = 1 + cos²x/sin²x (def of tanx) = (sin²x + cos²x)/sin²x = 1/sin²x. (pythagoric equation sin²x+cos²x=1)

As for the last step, sin²x(1/sin²x) = sin²x/sin²x = 1