TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right)\) then \(f\left(\frac{\pi}{5}\right)=\)
- A \(\frac{3(\sqrt{5}-1)}{16}\)
- B \(\frac{3 \sqrt{10-2 \sqrt{5}}}{8}\)
- C \(\frac{3 \sqrt{10+2 \sqrt{5}}}{8}\)
- D \(\frac{3(\sqrt{5}+1)}{16}\)
Answer & Solution
Correct Answer
(D) \(\frac{3(\sqrt{5}+1)}{16}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \quad f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right) \\ & \cos \left(\theta-\frac{2 \pi}{3}\right)=\cos \left(\pi-\left(\frac{\pi}{3}+\theta\right)\right)=\cos \left(\pi+\frac{\pi}{3}+\theta\right)…
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