Question

20 POINTS, please help!!Factor the algebraic expression below in terms of a single trigonometric function.

csc ^2x-1

Answer 1

csc²x - 1

1/sin²x - 1

1/sin²x - sin²x / sin²x

(1 - sin²x) / sin²x

Recall that sin²x + cos²x = 1

So cos²x = 1 - sin²x

So we can replace numerator to cos²x

cos²x / sin²x

= cot²x

Final answer: cot²x