Help in turning (2/sin^2x)/(1/sin^2x-1) into 2sec^2x
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Help in turning (2/sin^2x)/(1/sin^2x-1) into 2sec^2x

[From: ] [author: ] [Date: 11-04-22] [Hit: ]
:|-This is actually not true. Unless you wrote down the problem wrong, simplifying the more complex part of this relation simplifies to -2*cot(x)^2.To begin, the sin(x)^2-1 on the denominator can simplify to -cos(x)^2, by the identity 1-sin(x)^2=cos(x)^2.......
I don't understand how to do this.
Help, please? :|

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This is actually not true. Unless you wrote down the problem wrong, simplifying the more complex part of this relation simplifies to -2*cot(x)^2. I will show you how:

To begin, the sin(x)^2-1 on the denominator can simplify to -cos(x)^2, by the identity 1-sin(x)^2=cos(x)^2.

This becomes:

(2/sin(x)^2) / (-1/cos(x)^2)

Multiply by the reciprocal:

(2/sin(x)^2) * (-cos(x)^2) = -2 * (cos(x)^2/sin(x)^2) = -2 cot(x)^2
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