Given $\cos\theta=\frac{4}{5}$cosθ=45 and $\sin\theta=\frac{3}{5}$sinθ=35:

a

Find the value of $\sin2\theta$sin2θ.

b

Find the value of $\cos2\theta$cos2θ.

c

Find the value of $\tan2\theta$tan2θ.

Easy

Approx 9 minutes

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Given $\cos\theta=\frac{4}{5}$cosθ=45 and $\sin\theta$sinθ$<$<$0$0, find:

Solve for the exact value of $\cos\left(\frac{x}{2}\right)$cos(x2) if $\cos x=\frac{2}{5}$cosx=25 and $00<x$<$<$\frac{\pi}{2}$π2. Express your solution in rationalised form.