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Question

Mathematics Question on Maxima and Minima

The maximum value of sin θ\theta cos θ\theta is

A

1

B

12\frac{1}{2}

C

12\frac{1}{\sqrt{2}}

D

32\frac{\sqrt{3}}{2}

Answer

12\frac{1}{2}

Explanation

Solution

Max. value of sin θ\theta cos θ\theta = Max . value of (sin2θ2)\left( \frac{sin 2 \theta}{2} \right) = 12\frac{1}{2} Max. value of sin 2 θ\theta = 12(1)=12\frac{1}{2}(1) = \frac{1}{2}