Review question

# Can we write $\sin\theta$ and $\cos\theta$ in terms of $\tan(\theta/2)$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6696

## Question

Prove that, if $t=\tan \tfrac{1}{2}\theta$, then $\sin\theta=\frac{2t}{1+t^2}\quad\text{and}\quad \cos\theta=\frac{1-t^2}{1+t^2}.$

By expressing $\dfrac{3+\cos\theta}{\sin\theta}$ in terms of $t$, or otherwise, show that this expression cannot have any value between $-2\sqrt{2}$ and $+2\sqrt{2}$.