JEE Mains · Maths · STD 11 - 9. straight line
Let the range of the function \(f(x)=6+16 \cos x \cdot \cos \left(\frac{\pi}{3}-x\right) \cdot \cos \left(\frac{\pi}{3}+x\right) \cdot \sin 3 x \cdot \cos 6 x, x \in \mathbf{R}\) be \([\alpha, \beta]\). Then the distance of the point \((\alpha, \beta)\) from the line \(3 x+4 y+12=0\) is :
- A 11
- B 8
- C 10
- D 9
Answer & Solution
Correct Answer
(A) 11
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x)=6+16 \cos x \cdot \cos \left(\frac{\pi}{3}-x\right) \\ & \qquad \cos \left(\frac{\pi}{3}+x\right) \cdot \sin 3 x \cdot \cos 6 x \\ & f(x)=6+4 \cos 3 x \cdot \sin 3 x \cdot \cos 6 x \\ & \therefore \quad f(x)=6+\sin 12 x \\ & \therefore \quad \text { Range…
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