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Prove that: sin 10^@sin 50^@sin 60^@sin...

Prove that: ` sin 10^@sin 50^@sin 60^@sin 70^@=(sqrt(3))/(16)`

Text Solution

Verified by Experts

We know that
`4 sin theta sin (60^circ+theta) sin (60^circ-theta)=sin 3 theta`
So,

`sin 10^circ sin 70^circ sin 50^circ sin 60^circ `
=`1/4` sin `(10 times 3)^circ times` sin `60^circ`
=`sqrt3/16`
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