# Factor the algebraic expression below in terms of a single trigonometric function. csc 2x - 1

Asked by maham237 @ in Advanced Placement (Ap) viewed by 2534 People

20 POINTS, please help!!Factor the algebraic expression below in terms of a single trigonometric function.
csc ^2x-1

Answered by maham237 @

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

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