Using \(\sin(A+B)\) and suitable double-angle identities, prove \(\sin3\theta=3\sin\theta-4\sin^3\theta\).[3]
Given \(\cos3\theta=4\cos^3\theta-3\cos\theta\), use \(\cos(A+B)\) with suitable \(A\) and \(B\) to prove \(\frac{\cos5\theta}{\cos\theta}=16\sin^4\theta-12\sin^2\theta+1\).[7]
By considering \(\frac{\cos5\theta}{\cos\theta}=0\), solve \(16\sin^4\theta-12\sin^2\theta+1=0\) for \(0\le\theta<\pi\), giving answers in the form \(\frac{n\pi}{10}\), \(n\in\mathbb N\).[4]
Find the four exact values of \(\sin\theta\) satisfying \(16\sin^4\theta-12\sin^2\theta+1=0\).[5]
Hence show that \(\sin\frac{\pi}{10}=\sqrt{\frac{3-\sqrt5}{8}}\).[3]
State the exact value of \(\sin\frac{7\pi}{10}\).[2]
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.