Prove that \(\frac{\cos^3x + \sin x \cos^2x + \cos x \sin^2x + \sin^3x}{1 + \cos 2x + \sin 2x}

Question

Prove that $\frac{\cos^3x + \sin x \cos^2x + \cos x \sin^2x + \sin^3x}{1 + \cos 2x + \sin 2x} = \frac{1}{2 \cos x}$.[3] Hence or otherwise, find all the angles between $0{}^\circ$ and $360{}^\circ$ inclusive which satisfy the equation $\frac{\cos^3x + \sin x \cos^2x + \cos x \sin^2x + \sin^3x}{1 + \cos 2x + \sin 2x} = 5 \cos x$.[5]

Accepted Answer

(i) $\dfrac1{2\cos x}$ (ii) $x=71.6^\circ,108.4^\circ,251.6^\circ,288.4^\circ$

NJC IP4 Further Trigonometric Identities Tutorial Q1

NJC IP4 Further Trigonometric Identities Tutorial Q1

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