Simplify the following expression sin1 -sin 2-sin 181-

We know that sin180^∘=0 #160;sin 1^∘ .sin 2^∘.sin 3^∘.....sin 181^∘=sin 1^∘.sin 2^∘.....sin 180^∘.sin 181^∘=0 ...

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Circular Measurement of Angle

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Question

Simplify the following expression $sin 1^{\circ} . sin 2^{\circ} . . . . . sin 181^{\circ}$

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Solution

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sin 1^{\circ} + sin 2^{\circ} + \dots \dots + sin 359^{\circ} + sin 360^{\circ}

\frac{2 (sin 1^{0} + sin 2^{0} + sin 3^{0} + . . . . . . . . + sin 89^{0})}{2 (cos 1^{0} + cos 2^{0} + . . . . . . . + cos 44^{0}) + 1}

sin 1^{\circ} sin 2^{\circ} sin 3^{\circ} . . . . . . sin 180^{\circ}

sin $1^{\circ}$ $\times$ sin $2^{\circ}$ $\times$ sin $3^{\circ}$ $\times$ …….. $\times$ sin $180^{\circ}$ is equal to:

x = sin 1, y = sin 2; z = sin 3

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