The length of the longest interval in which the function y = sin ⁡ 2 x - 2 sin ⁡ x increases for x ∈ 0 , π is

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The length of the longest interval in which the function

y = \sin 2 x - 2 \sin x

increases for

x \in [0, π]

is

MathematicsApplication of DerivativesJEE Main

Options:

A $\frac{π}{2}$
B $\frac{π}{3}$
C $\frac{2 π}{3}$
D $\frac{π}{6}$

Solution:

1113 Upvotes Verified Answer

The correct answer is:

\frac{π}{3}

\frac{d y}{d x} = 2 \cos 2 x - 2 c o s x

= 2 (2 c o s^{2} x - \cos x - 1)

= 2 (2 \cos x + 1) (\cos x - 1)

∴ y

increases in

(\frac{2 π}{3}, π)

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