New Zealand
Level 8 - NCEA Level 3

# Applications of angle sum and difference identities

## Interactive practice questions

By using the expansion of $\cos\left(A+B\right)$cos(A+B), verify $\cos2x=2\cos^2\left(x\right)-1$cos2x=2cos2(x)1.

Easy
Approx 5 minutes

By using the expansion of $\sin\left(A+B\right)$sin(A+B), verify that $\sin2x=2\sin x\cos x$sin2x=2sinxcosx.

By simplifying the left hand side (LHS) of the identity, verify that $\sin\left(x+y\right)-\sin\left(x-y\right)=2\cos x\sin y$sin(x+y)sin(xy)=2cosxsiny.

By simplifying the left hand side of the identity, verify that $\frac{\sin\left(x-y\right)}{\cos x\cos y}=\tan x-\tan y$sin(xy)cosxcosy=tanxtany

### Outcomes

#### M8-6

Manipulate trigonometric expressions

#### 91575

Apply trigonometric methods in solving problems