Find the value of $s i n 2^{0} . s i n 4^{0} . s i n 6^{0} . . . . . . . s i n 180^{0}$ .

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Solution

$sin 2^{o} . sin 4^{o} . sin 6^{o} . . . . . sin 180^{o}$
Since, $sin 180^{o} = 0$
Therefore,
$sin 2^{o} . sin 4^{o} . sin 6^{o} . . . . . . sin 180^{o} = 0$

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sin 20^{\circ} sin 40^{\circ} sin 60^{\circ} sin 80^{\circ} = \frac{k}{16}

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sin 20 \times sin 40 \times sin 60 \times sin 80

$s i n 20^{\circ} s i n 40^{\circ} s i n 60^{\circ} s i n 80^{\circ}$ =

sin 20 \cdot sin 40 \cdot sin 60. s i n 80

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