If x = cos 10^circ cos 20^circ cos 40^circ , | vedclass

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(B) Given: $x = \cos 10^\circ \cos 20^\circ \cos 40^\circ$Multiply and divide by $2 \sin 10^\circ$:$x = \frac{2 \sin 10^\circ \cos 10^\circ \cos 20^\c

Vedclass · Accepted Answer

$\frac{1}{8}\cot 10^\circ $

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(B) Given: $x = \cos 10^\circ \cos 20^\circ \cos 40^\circ$Multiply and divide by $2 \sin 10^\circ$:$x = \frac{2 \sin 10^\circ \cos 10^\circ \cos 20^\circ \cos 40^\circ}{2 \sin 10^\circ}$Using $2 \sin A \cos A = \sin 2A$:$x = \frac{\sin 20^\circ \cos 20^\circ \cos 40^\circ}{2 \sin 10^\circ}$Multiply and divide by $2$:$x = \frac{2 \sin 20^\circ \cos 20^\circ \cos 40^\circ}{4 \sin 10^\circ} = \frac{\sin 40^\circ \cos 40^\circ}{4 \sin 10^\circ}$Multiply and divide by $2$ again:$x = \frac{2 \sin 40^\circ \cos 40^\circ}{8 \sin 10^\circ} = \frac{\sin 80^\circ}{8 \sin 10^\circ}$Since $\sin 80^\circ = \cos 10^\circ$:$x = \frac{\cos 10^\circ}{8 \sin 10^\circ} = \frac{1}{8} \cot 10^\circ$.

If $x = \cos 10^\circ \cos 20^\circ \cos 40^\circ ,$ then the value of $x$ is

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