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Question
The value of sin 20° sin 40° sin 60° sin 80° is ______.
Options
`(-3)/16`
`5/16`
`3/16`
`1/16`
Solution
The value of sin 20° sin 40° sin 60° sin 80° is `3/16`.
Explanation:
Indeed sin 20° sin 40° sin 60° sin 80°.
= `sqrt(3)/2` sin 20° sin (60° – 20°) sin (60° + 20°) (since sin 60° = `sqrt(3)/2`)
= `sqrt(3)/2` sin 20° [sin260° – sin220°]
= `sqrt(3)/2 sin 20^circ [3/4 - sin^2 20^circ]`
= `sqrt(3)/2 xx 1/4` [3sin 20° – 4sin320°]
= `sqrt(3)/2 xx 1/4` (sin 60°)
= `sqrt(3)/2 xx 1/4 xx sqrt(3)/2`
= `3/16`
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