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Use identities to simplify 〖tan〗^2 θ〖csc〗^2 θ

Sagot :

LanceLongFei

Answer:

[tex]\frac{1}{\cos^2(\theta)}[/tex]

Step-by-step explanation:

We know that [tex]\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] and [tex]\csc(\theta) = \frac{1}{\sin(\theta)}[/tex] by definition. So

[tex]\tan^2(\theta) \cdot \csc^2(\theta) = \frac{\sin^2(\theta)}{\cos^2(\theta)} \cdot \frac{1}{\sin^2(\theta)} = \frac{1}{\cos^2(\theta)}[/tex].

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