Question

sin10°sin30°sin50°sin70°=1/16

Answer 1

Hey !!!

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$\underline{rajukumar111}$
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Answer 2

$sin10sin30sin50sin70 \\ \\ = \frac{1}{2} sin10sin50sin70\\ \\ = \frac{1}{2} \times \frac{1}{2} (2sin10sin50)sin70 \\ \\ = \frac{1}{4} (cos(10 - 50) - cos(10 + 50))sin70 \\ \\ = \frac{1}{4} (cos40 - cos60)sin70 \\ \\ = \frac{1}{4} (cos40sin70 - \frac{1}{2} sin70) \\ \\ = \frac{1}{8} (2cos40sin70 - sin70) \\ \\ = \frac{1}{8} (sin(40 + 70) - sin(40 - 70) - sin70) \\ \\ = \frac{1}{8} (sin110 + sin30 - sin70) \\ \\ = \frac{1}{8} (sin(90 + 20) + sin30 - sin(90 - 20)) \\ \\ = \frac{1}{8} (cos20 + \frac{1}{2} - cos20) \\ \\ = \frac{1}{8} \times \frac{1}{2} \\ \\ = \frac{1}{16}$