MHT CET · Maths · Trigonometric Equations
The value of \(4 \cos ^3 20^{\circ}\) is
- A \(-\frac{1}{2}-\cos 20^{\circ}\)
- B \(-\frac{1}{2}+3 \cos 20^{\circ}\)
- C \(\frac{1}{2}+3 \cos 20^{\circ}\)
- D \(\frac{1}{2}-3 \cos 20^{\circ}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}+3 \cos 20^{\circ}\)
Step-by-step Solution
Detailed explanation
\(4 \cos ^3 20^{\circ}=\cos \left(3 \times 20^{\circ}\right)+3 \cos 20^{\circ}[\because 4 \cos ^3 \theta=\cos 3 \theta\)\(+3 \cos \theta]\)
\(\Rightarrow 4 \cos ^3 20^{\circ}=\cos 60^{\circ}+3 \cos 20^{\circ}=\frac{1}{2}+3 \cos 20^{\circ}\)
\(\Rightarrow 4 \cos ^3 20^{\circ}=\cos 60^{\circ}+3 \cos 20^{\circ}=\frac{1}{2}+3 \cos 20^{\circ}\)
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