Simplifying trigonometric expressions help?

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06-04-2018
Mathematics

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Simplifying trigonometric expressions help?

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The question is down below. Thank you.

WojtekR WojtekR · Answer 1 · 2018-04-06T18:15:17+02:00

7.

[tex]\dfrac{\sin\theta\cdot\cot\theta}{\tan\theta\cdot\cos\theta}=\dfrac{\sin\theta}{\cos\theta}\cdot\dfrac{1}{\tan\theta}\cdot\cot\theta=\tan\theta\cdot\dfrac{1}{\tan\theta}\cdot\cot\theta=\boxed{\cot\theta}[/tex]

8.

[tex]\dfrac{\cot\theta}{\cos\theta}\cdot\dfrac{\sin\theta\cdot\cos^2\theta}{1-\cos^2\theta}=\dfrac{\cot\theta}{\cos\theta}\cdot\dfrac{\sin\theta\cdot\cos^2\theta}{\sin^2\theta}=\cot\theta\cdot\dfrac{\cos\theta}{\sin\theta}=\cot\theta\cdot\cot\theta=\\\\\\=\boxed{\cot^2\theta}[/tex]