Let the range of the function f(x) = 6 + 16 cos x · cos ((π)/3 - x) · cos ((π)/3 + x) · sin 3x · cos 6x, x R be [α, β]. Then the distance of the point (α, β) from the line 3x + 4y + 12 = 0 is:

Trigonometry: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q236

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumTrigonometry118× since 2002

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 3x \cdot \cos 6x

x \in \mathbf{R}

[\alpha, \beta]

. Then the distance of the point

(\alpha, \beta)

from the line

3x + 4y + 12 = 0

is:

JEE Main 2025 Trigonometry Question with Solution (January Unspecified (session-level dataset), Q236) | JEE Arc

JEE Main 2025 · January, Unspecified (session-level dataset) · Q236

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumTrigonometry118× since 2002

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 3x \cdot \cos 6x

x \in \mathbf{R}

[\alpha, \beta]

. Then the distance of the point

(\alpha, \beta)

from the line

3x + 4y + 12 = 0

is: