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Ostrovityanka [42]
3 years ago
8

Simplify the trigonometric function

Mathematics
1 answer:
Alisiya [41]3 years ago
8 0

Answer:

  a.  csc²θ

Step-by-step explanation:

You can use the identities ...

  1 +tan² = sec²

  cot = cos/sin

  sec = 1/cos

  csc = 1/sin

___

Then the expression becomes ...

  \cot^2{\theta}(1+\tan^2{\theta})=\cot^2{\theta}\sec^2{\theta}=\dfrac{\cos^2{\theta}}{\sin^2{\theta}\cos^2{\theta}}=\dfrac{1}{\sin^2{\theta}}\\\\=\boxed{\csc^2{\theta}}

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