Question

Solve trigonometric function
sin∅ + cos∅ × cot∅

Answer 1

`\csc(\theta)`

Explanation:

`\cot(\theta)=(1)/(\tan(\theta))=(\cos(\theta))/(\sin(\theta))`

`\sin^2(\theta)+\cos^2(\theta)=1`

`\implies \sin(\theta)+\cos(\theta)*\cot(\theta)=\sin(\theta)+\cos(\theta)*(\cos(\theta))/(\sin(\theta))`

`=\sin(\theta)+(\cos^2(\theta))/(\sin(\theta))`

`=(\sin^2(\theta))/(\sin(\theta))+(\cos^2(\theta))/(\sin(\theta))`

`=(\sin^2(\theta)+\cos^2(\theta))/(\sin(\theta))`

`=(1)/(\sin(\theta))`

`=\csc(\theta)`