If frac{1-10 i cos theta}{1-10 sqrt{3} i sin | vedclass

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(A) To make the expression purely real,its imaginary part must be zero. Let $z = \frac{1-10 i \cos 	heta}{1-10 \sqrt{3} i \sin 	heta}$. Multiply the

Vedclass · Accepted Answer

$\frac{\pi}{6}$

Vedclass · Answer

(A) To make the expression purely real,its imaginary part must be zero. Let $z = \frac{1-10 i \cos 	heta}{1-10 \sqrt{3} i \sin 	heta}$. Multiply the numerator and denominator by the conjugate of the denominator: $z = \frac{(1-10 i \cos 	heta)(1+10 \sqrt{3} i \sin 	heta)}{(1-10 \sqrt{3} i \sin 	heta)(1+10 \sqrt{3} i \sin 	heta)}$ $z = \frac{1 + 10 \sqrt{3} i \sin 	heta - 10 i \cos 	heta + 100 \sqrt{3} \sin 	heta \cos 	heta}{1 + 300 \sin^2 	heta}$ The imaginary part is $\frac{10 \sqrt{3} \sin 	heta - 10 \cos 	heta}{1 + 300 \sin^2 	heta}$. Setting the imaginary part to $0$: $10 \sqrt{3} \sin 	heta - 10 \cos 	heta = 0$ $10 \sqrt{3} \sin 	heta = 10 \cos 	heta$ $	an 	heta = \frac{10}{10 \sqrt{3}} = \frac{1}{\sqrt{3}}$ Since $	an 	heta = \frac{1}{\sqrt{3}}$,we have $	heta = \frac{\pi}{6}$.

If $\frac{1-10 i \cos \theta}{1-10 \sqrt{3} i \sin \theta}$ is purely real,then one of the values of $\theta$ is

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