TS EAMCET · Maths · Trigonometric Equations
If \(f(x)=\cos ^2 x+\cos ^2 2 x+\cos ^2 3 x\), then the number of values of \(x \in[0,2 \pi]\) for which \(f(x)=1\) is
- A 4
- B 6
- C 8
- D 10
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x)=\cos ^2 x+\cos ^2 2 x+\cos ^2 3 x=1 \\ & \Rightarrow \cos ^2 x+\left(2 \cos ^2 x-1\right)^2+\left(4 \cos ^3 x-3 \cos x\right)^2=1 \\ & \Rightarrow \cos ^2 x+4 \cos ^4 x+1-4 \cos ^2 x+16 \cos ^6 x \\ & +9 \cos ^2 x-24 \cos ^4 x=1 \\ & \Rightarrow \quad 6…
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