Question

If $5\cos x+12\cos y=13$, then the maximum value of $5\sin x+12\sin y$ is :

• A. $12$
• B. $\sqrt{120}$
• C. $\sqrt{20}$
• D. $13$

Answer 1

Answer: (B)

$\because 5\cos x+12\cos y=13$
$\Rightarrow (5\cos x+12\cos y{)}^2=169$
$\therefore (5\cos x+12\cos y{)}^2+(5\sin x+12\sin y{)}^2$
$\Rightarrow (13{)}^2+(5\sin x+12\sin y{)}^2$
$=25+144+120(\sin x\sin y+\cos x\cos y)$
$\Rightarrow (5\sin x+12\sin y{)}^2=120\cos (x-y)$
$\because -1\le \cos (x-y)\le 1$
$\therefore$ Maximum value of $5\sin x+12\sin y$
$=\sqrt{120}$