Question

Given costheta • csctheta - 2costheta = 0, solve for theta (May be multiple answers)

Answer 1

Factor out
`\cos\theta`:

`\cos\theta\csc\theta-2\cos\theta=\cos\theta(\csc\theta-2)=\cos\theta\left(\frac1{\sin\theta}-2\right)=0`

Then either

`\cos\theta=0\implies\theta=\frac\pi2+n\pi`

or

`\frac1{\sin\theta}-2=0\implies\sin\theta=\frac12\implies\theta=\frac\pi6+2n\pi\text{ or }\theta=\frac{5\pi}6+2n\pi`

where
`n` is any integer.