NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Apply double and half angle identities

## Interactive practice questions

By simplifying the left hand side ($LHS$LHS) of the identity, prove that $\frac{1-\cos2x}{\sin2x}=\tan x$1cos2xsin2x=tanx.

Easy
Approx 6 minutes

By simplifying the left hand side ($LHS$LHS) of the identity, prove that $\frac{2\tan A}{1+\tan^2\left(A\right)}=\sin2A$2tanA1+tan2(A)=sin2A.

By simplifying the left hand side ($LHS$LHS) of the identity, prove that $\frac{2\sin^3\left(x\right)+2\cos^3\left(x\right)}{\sin x+\cos x}=2-\sin2x$2sin3(x)+2cos3(x)sinx+cosx=2sin2x, for $\sin x+\cos x\ne0$sinx+cosx0.

### Outcomes

#### M8-6

Manipulate trigonometric expressions

#### 91575

Apply trigonometric methods in solving problems