Question

If $x$ and $y$ are both non-negative and if $x+y=\pi$, then the maximum value of $5\sin x\sin y$ is equal to

• A. 1
• B. $\sqrt{5}$
• C. 5
• D. $-5$
• E. 0

Answer 1

Answer: (C)

$f(x)=5\sin x\cdot \sin y$
$f(x)=5\sin x\sin (\pi -x)$
$=5\sin x\cdot \sin x$
$f(x)=5{\sin }^{2}x$
$f^{\prime }(x)=0\sin 2x=0$
$f^{\prime }(x)=0\sin 2x=0$
$x=\pi /2$
$\Rightarrow 5$