Question

If x + y = `pi/2`, then the maximum value of sin x. sin y is.

Options

• \[\frac{1}{2}\]

• `(-1)/sqrt2`

• `1/sqrt2`

• `(-1)/2`

Answer 1

\[\frac{1}{2}\]

Explanation:

We have,

x + y = `pi/2`

∴ sin x sin y = sin x sin `(pi/2 - x) = sin x cos x = 1/2`sin 2x

∴ Maximum value of sin x sin y = `1/2`