Evaluate: sin 21^{circ} cos 9^{circ}-cos 84^{ | vedclass

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Question

(B) Given expression: $\sin 21^{\circ} \cos 9^{\circ}-\cos 84^{\circ} \cos 6^{\circ}$ Using the identity $\cos 84^{\circ} = \sin(90^{\circ}-84^{\circ}

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(B) Given expression: $\sin 21^{\circ} \cos 9^{\circ}-\cos 84^{\circ} \cos 6^{\circ}$ Using the identity $\cos 84^{\circ} = \sin(90^{\circ}-84^{\circ}) = \sin 6^{\circ}$,the expression becomes: $\sin 21^{\circ} \cos 9^{\circ}-\sin 6^{\circ} \cos 6^{\circ}$ Multiply and divide by $2$: $= \frac{1}{2} [2 \sin 21^{\circ} \cos 9^{\circ} - 2 \sin 6^{\circ} \cos 6^{\circ}]$ Using $2 \sin A \cos B = \sin(A+B) + \sin(A-B)$ and $2 \sin 	heta \cos 	heta = \sin 2	heta$: $= \frac{1}{2} [(\sin(21^{\circ}+9^{\circ}) + \sin(21^{\circ}-9^{\circ})) - \sin(2 	imes 6^{\circ})]$ $= \frac{1}{2} [\sin 30^{\circ} + \sin 12^{\circ} - \sin 12^{\circ}]$ $= \frac{1}{2} [\sin 30^{\circ}]$ $= \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{4}$

Evaluate: $\sin 21^{\circ} \cos 9^{\circ}-\cos 84^{\circ} \cos 6^{\circ}$

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