Question

Q6. Prove that: sin 20 sin 40 sin 60 sin 80 = 3/16

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

sin20° sin40° sin60° sin80°

=>. sin 60° sin20° sin40° sin80°

=>. √3/2 sin 20° sin40° sin80°

=>. √3/2 ×1/2 [2sin20° sin40°] sin80°

=>. √3/4 [ cos(40-20) - cos(20+40) ] sin 80°

=>. √3/4 [cos20° - cos60°] sin80°

=>. √3/4 cos20°sin80° - √3/4 cos60°sin80°

=>. √3/4 × 1/2 [2 cos20° sin80°] - √3/4×1/2 sin80°

=>. √3/8 [sin(20+80) -sin(20-80)] - √3/8 sin80°

=>. √3/8 [sin100° - sin(-60°)] - √3/8 sin80°

=>. √3/8 sin100° - √3/8 sin(-60°) - √3/8 sin80°

=>. √3/8 sin(180 - 80) + √3/8 × √3/2 - √3/8 sin80°

=>. √3/8 sin80° + 3/16 - √3/8 sin80°

=>. 3/16 hence proved....

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