Question

Simplifying trigonometric expressions help?

Answer 1

7.


`(\sin\theta\cdot\cot\theta)/(\tan\theta\cdot\cos\theta)=(\sin\theta)/(\cos\theta)\cdot(1)/(\tan\theta)\cdot\cot\theta=\tan\theta\cdot(1)/(\tan\theta)\cdot\cot\theta=\boxed{\cot\theta}`

8.


`(\cot\theta)/(\cos\theta)\cdot(\sin\theta\cdot\cos^2\theta)/(1-\cos^2\theta)=(\cot\theta)/(\cos\theta)\cdot(\sin\theta\cdot\cos^2\theta)/(\sin^2\theta)=\cot\theta\cdot(\cos\theta)/(\sin\theta)=\cot\theta\cdot\cot\theta=\\\\\\=\boxed{\cot^2\theta}`