Using $\sin 3x = \sin(2x + x)$, show that $\sin 3x = 3 \sin x - 4 \sin^3 x$.[4] Solve the equati

Question

Using $\sin 3x = \sin(2x + x)$, show that $\sin 3x = 3 \sin x - 4 \sin^3 x$.[4] Solve the equation $\tan^2 x - 2 = \frac{-2}{\cos x}$ for $0 \le x \le 2\pi$.[5] In the diagram, $AB$ is a diameter of a circle centre $O$ and $\sin \angle CAB = p$. Find, in terms of $p$, the value of $\tan \angle ABC$,[2] $\cos \angle BOC$.[2]

Accepted Answer

(a) $\sin3x=3\sin x-4\sin^3x$ (b) $x=0,\ 1.91,\ 4.37,\ 2\pi\text{ rad}$ (c)(i) $\dfrac{\sqrt{1-p^2}}{p}$ (ii) $1-2p^2$

2023 ACSBR AM S3 EOY Q13

2023 ACSBR AM S3 EOY Q13

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