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Taking θ = 30°, verify that : sin3θ = 3 sinθ – 4 sin3θ |
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Answer» To verify : sin3 = 3sin – 4 sin3 Given that = 30° L.H.S = sin 3 = sin (3× 30°) = sin(90°) = 1. (∵ sin90° = 1) R.H.S = 3 sin – 4sin3 = 3sin30° – 4 sin330° 3 x \(\frac{1}{2} - 4(\frac{1}{2})^3\) (\(\because sin 30° = 1\)) \(\frac{3}{2} - \frac{4}{8} = \frac{3}{2} - \frac{1}{2} = \frac{2}{2} = 1.\) Hence, L.H.S = R.H.S. Therefore, for =30°, sin3 = 3sin – 4sin3. Hence Proved |
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