Let the range of the function f ( x ) = 6 + 16 cos x ⋅ cos ( 3 π − x ) ⋅ cos ( 3 π + x ) ⋅ sin 3 x ⋅ cos 6 x , x ∈ R be [ α , β ] . Then the distance of the point ( α , β ) from the line 3 x + 4 y

Question

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

TestHub · Accepted Answer

​ f ( x ) = 6 + 16 cos x ⋅ cos ( 3 π ​ − x ) cos ( 3 π ​ + x ) ⋅ sin 3 x ⋅ cos 6 x f ( x ) = 6 + 4 cos 3 x ⋅ sin 3 x ⋅ cos 6 x ∴ f ( x ) = 6 + sin 12 x ∴ Range of f ( x ) = [ 5 , 7 ] ∴ [ α , β ] = [ 5 , 7 ] ​ ∴ Distance of point from 3 x + 4 y + 12 = 0 ​ = ​ 3 2 + 4 2 ​ 3.5 + 4.7 + 12 ​ ​ = 11 units ​

Mathematics - Functions Question with Solution | TestHub

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