The value of cos 15^{circ} cos 7.5^{circ} sin | vedclass

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Question

(B) We are given the expression: $\cos 15^{\circ} \cos 7.5^{\circ} \sin 7.5^{\circ}$.Using the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$, we

Vedclass · Accepted Answer

$\frac{1}{8}$

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(B) We are given the expression: $\cos 15^{\circ} \cos 7.5^{\circ} \sin 7.5^{\circ}$.Using the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$, we can write $\sin 7.5^{\circ} \cos 7.5^{\circ} = \frac{1}{2} \sin(2 	imes 7.5^{\circ}) = \frac{1}{2} \sin 15^{\circ}$.Substituting this into the original expression:$\cos 15^{\circ} 	imes (\frac{1}{2} \sin 15^{\circ}) = \frac{1}{2} \sin 15^{\circ} \cos 15^{\circ}$.Again, using the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$, we have $\sin 15^{\circ} \cos 15^{\circ} = \frac{1}{2} \sin(2 	imes 15^{\circ}) = \frac{1}{2} \sin 30^{\circ}$.Thus, the expression becomes $\frac{1}{2} 	imes (\frac{1}{2} \sin 30^{\circ}) = \frac{1}{4} \sin 30^{\circ}$.Since $\sin 30^{\circ} = \frac{1}{2}$, the final value is $\frac{1}{4} 	imes \frac{1}{2} = \frac{1}{8}$.

The value of $\cos 15^{\circ} \cos 7.5^{\circ} \sin 7.5^{\circ}$ is

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