Question

Simplify the trigonometric function

Answer 1

a. csc²θ

Explanation:

You can use the identities ...

1 +tan² = sec²

cot = cos/sin

sec = 1/cos

csc = 1/sin

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Then the expression becomes ...

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