#2015_11 My class test problem -2

Geometry Level 4

$\large 12\sin(x)+5\cos(x)=2y^{ 2 }-8y+21$

If $x$ and $y$ are the solutions of the equation above, then what is the value of $12\cot\left( \frac { xy }{ 2 } \right)$ ?

1 solution

Anand O R
Jun 2, 2015

$12sinx+5cosx \leq 13$ and $2y^{ 2 }-8y+21 \geq 13$

$\Rightarrow$ $12sinx+5cosx=2y^{ 2 }-8y+21=13$

After solving , $x=cot^{-1}\left( \frac { 5 }{ 12 } \right)$ and $y=2$

Therefore , $12cot\left( \frac { xy }{2 } \right) = \boxed{5}$

Almost right. Is is true that $x = \cot^{-1} \frac 5{12}$ only?

@CR Ãnänd Nice solution!

Anandhu Raj - 6 years ago