TS EAMCET · Maths · Trigonometric Ratios & Identities
The solution set of \((5+4 \cos \theta)(2 \cos \theta+1)=0\) in the interval \([0,2 \pi]\), is :
- A \(\left\{\frac{\pi}{3}, \frac{2 \pi}{3}\right\}\)
- B \(\left\{\frac{\pi}{3}, \pi\right\}\)
- C \(\left\{\frac{2 \pi}{3}, \frac{4 \pi}{3}\right\}\)
- D \(\left\{\frac{2 \pi}{3}, \frac{5 \pi}{3}\right\}\)
Answer & Solution
Correct Answer
(C) \(\left\{\frac{2 \pi}{3}, \frac{4 \pi}{3}\right\}\)
Step-by-step Solution
Detailed explanation
We have, \((5+4 \cos \theta)(2 \cos \theta+1)=0\)...(i) \(\cos \theta=\frac{1-\tan ^2 \frac{\theta}{2}}{1+\tan ^2 \frac{\theta}{2}}\) \(\therefore \quad \cos \theta=\frac{1-t^2}{1+t^2} \quad\left[\right.\) put \(\left.\tan \frac{\theta}{2}=t\right]\) Then, Eq. (i) becomes…
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