Question

Prove (csc²ˣ-1)/(cos(x))=cot(x)csc(x)

Answer 1

To prove the given equation, (csc²ˣ-1)/(cos(x))=cot(x)csc(x), we can simplify both sides of the equation step by step.

Step-by-step explanation:

To prove the given equation: (csc²x-1)/(cos(x))=cot(x)csc(x)

We will start with the left side of the equation and simplify it:
(csc²x-1)/(cos(x))
= (1/sin²x-1)/(cos(x))
= 1/(sin²x-1) * 1/cos(x)
= 1/cos(x) * 1/(1 - sin²x)
= 1/cos(x) * 1/(cos²x)
= 1/cos(x) * 1/cos²x
= 1/cos(x) * cot²x
= cot(x)csc(x)

Therefore, the left side of the equation is equal to the right side, and the given equation has been proven.