This problem asks students to use a right-angled triangle to derive expressions for $\tan 2 \theta$, $\sin 2 \theta$ and $\cos 2 \theta$ in terms of $\tan \theta$.

Students will need to use:

• Angle sum of triangle
• Pythagoras's theorem
• Right-angled trig

You can download a Word and PDF version of this problem.

Students who are studying matrices might like to see how this result is used in the problem Reflect Again.