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zheka24 [161]
3 years ago
8

(cot^2x - 1)/(csc^2x) = cos2x​

Mathematics
1 answer:
Alex787 [66]3 years ago
5 0

Answer:

Step-by-step explanation:

The idea here is to get the left side simplified down so it is the same as the right side. Consequently, there are 3 identities for cos(2x):

cos(2x)=cos^2x-sin^2x,

cos(2x)=1-2sin^2x, and

cos(2x)=2cos^2x-1

We begin by rewriting the left side in terms of sin and cos, since all the identities deal with sines and cosines and no cotangents or cosecants.  Rewriting gives you:

\frac{\frac{cos^2x}{sin^2x} -\frac{sin^2x}{sin^2x} }{\frac{1}{sin^2x} }

Notice I also wrote the 1 in terms of sin^2(x).

Now we will put the numerator of the bigger fraction over the common denominator:

\frac{\frac{cos^2x-sin^2x}{sin^2x} }{\frac{1}{sin^2x} }

The rule is bring up the lower fraction and flip it to multiply, so that will give us:

\frac{cos^2x-sin^2x}{sin^2x} *\frac{sin^2x}{1}

And canceling out the sin^2 x leaves us with just

cos^2x-sin^2x which is one of our identities.

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