The value of (sin 210^{circ})(sin 585^{circ}) | vedclass

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Question

(A) We know that $\sin(180^{\circ} + 	heta) = -\sin 	heta$ and $\sin(540^{\circ} + 	heta) = \sin(360^{\circ} + 180^{\circ} + 	heta) = \sin(180^{\c

Vedclass · Accepted Answer

$\frac{1}{2 \sqrt{2}}$

Vedclass · Answer

(A) We know that $\sin(180^{\circ} + 	heta) = -\sin 	heta$ and $\sin(540^{\circ} + 	heta) = \sin(360^{\circ} + 180^{\circ} + 	heta) = \sin(180^{\circ} + 	heta) = -\sin 	heta$. Step $1$: Simplify $\sin 210^{\circ} = \sin(180^{\circ} + 30^{\circ}) = -\sin 30^{\circ} = -\frac{1}{2}$. Step $2$: Simplify $\sin 585^{\circ} = \sin(540^{\circ} + 45^{\circ}) = -\sin 45^{\circ} = -\frac{1}{\sqrt{2}}$. Step $3$: Multiply the values: $(-\frac{1}{2}) 	imes (-\frac{1}{\sqrt{2}}) = \frac{1}{2 \sqrt{2}}$. Thus,the correct option is $A$.

The value of $(\sin 210^{\circ})(\sin 585^{\circ})$ is

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