TS EAMCET · Maths · Complex Number
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
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \frac{1-10 i \cos \theta}{1-10 \sqrt{3} i \sin \theta} \times \frac{1+10 \sqrt{3} i \sin \theta}{1+10 \sqrt{3} i \sin \theta} \\ & =\frac{1+10 \sqrt{3} i \sin \theta-10 i \cos \theta+100 \sqrt{3} \sin \theta \cos \theta}{1+300 \sin ^2 \theta} \\ &…
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