JEE Mains · Maths · STD 11 - Trigonometrical equations
Let \(S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }\) If \(T =\sum_{\theta \in S } \cos 2 \theta\), then \(T + n ( S )\) is equal
- A \(7+\sqrt{3}\)
- B \(9\)
- C \(8+\sqrt{3}\)
- D \(10\)
Answer & Solution
Correct Answer
(B) \(9\)
Step-by-step Solution
Detailed explanation
\(\sin \theta \tan \theta+\tan \theta=\sin 2 \theta\) \(\tan \theta(\sin \theta+1)=\frac{2 \tan \theta}{1+\tan ^{2} \theta}\) \(\tan \theta=0 \Rightarrow \theta=-\pi, 0, \pi\) \((\sin \theta+1)=2 \cdot \cos ^{2} \theta=2(1+\sin \theta)(1-\sin \theta)\) \(\sin \theta=-1\) which…
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