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Lyrx [107]
3 years ago
14

Verify the pythagorean identity 1 + c o t ^2 θ = c s c ^2 θ

Mathematics
1 answer:
Grace [21]3 years ago
6 0

Answer: The identity is verified. See the explanation.

Step-by-step explanation:

You must keep on mind the following identities:

csc\theta=\frac{cos\theta}{sin\theta}\\\\csc\theta=\frac{1}{sin\theta}\\\\sin^2\theta+cos^2\theta=1

Therefore, by substitution, you can rewrite the identity as shown below:

1+cot^2\theta=csc^2\theta\\\\1+\frac{cos^2\theta}{sin^2\theta}=csc^2\theta

Simpliying, you obtain:

\frac{sin^2\theta+cos^2\theta}{sin^2\theta}=csc^2\theta\\\\\frac{1}{sin^2\theta}=csc^2\theta\\\\csc^2\theta=csc^2\theta

The identity is verified.

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