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Find:\( \sin \left(2 \cos ^{-1} \frac{4}{5}\right) \) |
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Answer» Let 2 cos-1\(\frac45=\theta\) ⇒ cos \(\frac{\theta}2=\frac45\) \(\therefore\) sin \(\frac{\theta}2=\frac35\) Now, sin θ = 2 sin θ/2 cos θ/2 = 2. 3/5. 4/5 = 24/25 θ = sin-1(24/25) \(\therefore\) 2 cos-1 4/5 = sin-1(24/25) \(\therefore\) sin (2 cos-14/5) = sin (sin-1(24/25)) = 24/25 |
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