WBJEE · Maths · Trigonometric Equations
If \(5 \cos 2 \theta+2 \cos ^2 \frac{\theta}{2}+1=0\), when \((0 < \theta < \pi)\), then the values of \(\theta\) are :
- A \(\frac{\pi}{3} \pm \pi\)
- B \(\frac{\pi}{3}, \cos ^{-1}\left(\frac{3}{5}\right)\)
- C \(\cos ^{-1}\left(\frac{3}{5}\right) \pm \pi\)
- D \(\frac{\pi}{3}, \pi-\cos ^{-1}\left(\frac{3}{5}\right)\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{3}, \pi-\cos ^{-1}\left(\frac{3}{5}\right)\)
Step-by-step Solution
Detailed explanation
Hints : \(5 \cos 2 \theta+1+\cos \theta+1=0\) \[ \begin{aligned} & 5\left(2 \cos ^2 \theta-1\right)+\cos \theta+2=0 \\ & 10 \cos ^2 \theta+\cos \theta-3=0 \\ & (5 \cos \theta+3)(2 \cos \theta-1)=0 \\ & \cos \theta=\frac{1}{2} \\ & \theta=\frac{\pi}{3} \end{aligned} \]…
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