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ziro4ka [17]
3 years ago
13

(csc x - 1) (csc x + 1)

Mathematics
1 answer:
victus00 [196]3 years ago
4 0
<h2>Explanation:</h2>

Here we have the following expression:

(csc x - 1) (csc x + 1)

So we need to extend this. Remember that the difference of squares tells us:

(a-b)(a+b)=a^2-b^2

So here:

a=cscx \\ \\ b=1

Thus:

(csc x - 1) (csc x + 1)=csc^2x-1 \\ \\ \\ But: \\ \\ cscx=\frac{1}{sinx} \\ \\ \\ Then: \\ \\ csc^2x-1=\frac{1}{sin^2x}-1=\frac{1-sin^2x}{sin^2x}=\frac{cos^2x}{sin^2x}=cot^2x \\ \\ \\ Finally: \\ \\ \boxed{(csc x - 1) (csc x + 1)=cot^2x}

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