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

## Question

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

2. 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 $360^\circ$.