Question

Solve trigonometric function

2csc∅- 2cos^2 ∅ ×csc∅

Answer 1

• Theta turned to A

`\\ \rm\Rrightarrow 2cscA-2cos^2A(cscA)`

`\\ \rm\Rrightarrow 2(1/sinA)-2cos^2A(1/sinA)`

`\\ \rm\Rrightarrow (2)/(sinA)-(2cos^2A)/(sinA)`

`\\ \rm\Rrightarrow (2-2cos^2A)/(sinA)`

`\\ \rm\Rrightarrow (2(1-cos^2A))/(sinA)`

`\\ \rm\Rrightarrow (2sin^2A)/(sinA)`

`\\ \rm\Rrightarrow sinA`

Answer 2

`2\sin(\theta)`

Explanation:

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

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

`2\csc(\theta)- 2cos^2(\theta)* csc(\theta)`

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

`=( 2[1-cos^2(\theta)])/(\sin(\theta))`

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

`=2\sin(\theta)`