Review question

# Can we write $\cos \theta - 2 \cos 3 \theta + \cos 5\theta$ using $\sin$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6120

## Suggestion

1. Prove the identity $\cos \theta - 2 \cos 3 \theta + \cos 5\theta = 2\sin \theta (\sin 2 \theta - \sin 4 \theta).$

Can we combine two $\cos$ terms using an expression for the difference of two cosines?

We could use this twice here…

1. Solve the equations

1. $\cos 2x = \sin x$,

2. $3 \sec^2 x = \tan x + 5$

giving in each case all solutions between $0^\circ$ and $360^\circ$.

Can we write the first equation just in terms of $\sin x$?

How can we relate $\sec^2 x$ to $\tan x$?

This would reduce the equations to quadratic ones…