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 The length of a longest interval in which the function 3sinx4sin3x is incresing is

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a
π/3
b
π/2
c
3π/2
d
π

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detailed solution

Correct option is A

Since 3sin⁡x−4sin3⁡x=sin⁡3x and sin⁡3x increases when 3x takes values from −π/2 to π/2 or x takes values from −π/6 to π/6. Thus, the length of the longest interval in  which 3sin⁡x−4sin3⁡x increases is π/6−(−π/6)=π/3.


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