Question

I NEED HELP PLEASEEEEE

Answer 1

Option (3)

Explanation:

`\text{tan}((\theta)/(2))=\text{sin}\theta`

`\text{tan}((\theta)/(2))=2\text{sin}{(\theta)/(2)} \text{cos}((\theta)/(2))`

`\frac{\text{sin}(\theta)/(2)}{\text{cos}(\theta)/(2)} =2\text{sin}{(\theta)/(2)}\text{cos}((\theta)/(2))`

`\text{sin(\theta)/(2)}=2\text{sin}{(\theta)/(2)}\text{cos}^2((\theta)/(2))`
`\text{sin(\theta)/(2)}=2\text{sin}{(\theta)/(2)}\text{cos}^2((\theta)/(2))`
`\text{sin}(\theta)/(2)=2\text{sin}{((\theta)/(2))}\text{cos}^2((\theta)/(2))`

`\text{sin}(\theta)/(2)-2\text{sin}{((\theta)/(2))}\text{cos}^2((\theta)/(2))=0`

`\text{sin}(\theta)/(2)[1-2\text{cos}^2((\theta)/(2))]=0`

`\text{sin}(\theta)/(2)=0` ⇒
`\theta=0`

`1-2\text{cos}^2((\theta)/(2))=0`

`\text{cos}((\theta)/(2))=(1)/(√(2))`

`(\theta)/(2)=(\pi)/(4)`

`\theta=(\pi)/(2)`

Therefore, θ = 0 and
`(\pi)/(2)` are the solutions.

Option (3) will be the answer.