Question

Simplifying trigonometric expressions help?

Answer 1

7.

$\dfrac{\sin\theta\cdot\cot\theta}{\tan\theta\cdot\cos\theta}=\dfrac{\sin\theta}{\cos\theta}\cdot\dfrac{1}{\tan\theta}\cdot\cot\theta=\tan\theta\cdot\dfrac{1}{\tan\theta}\cdot\cot\theta=\boxed{\cot\theta}$

8.

$\dfrac{\cot\theta}{\cos\theta}\cdot\dfrac{\sin\theta\cdot\cos^2\theta}{1-\cos^2\theta}=\dfrac{\cot\theta}{\cos\theta}\cdot\dfrac{\sin\theta\cdot\cos^2\theta}{\sin^2\theta}=\cot\theta\cdot\dfrac{\cos\theta}{\sin\theta}=\cot\theta\cdot\cot\theta=\\\\\\=\boxed{\cot^2\theta}$