Question

The number of pairs (x,y) satisfying the equation $sinx+siny=sin(x+y)$, $\left|x\right|+\left|y\right|=1$is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is C

6

$|x|+|y|-1|x|+|y|-1sinx+siny-sin(x+y)\Rightarrow 2sin\left(\frac{x+y}{2}\right)cos\left(\frac{x-y}{2}\right)-2sin\left(\frac{x+y}{2}\right).cos\left(\frac{x+y}{2}\right)\Rightarrow sin\left(\frac{x+y}{2}\right)=0\text{OR}cos\left(\frac{x+y}{2}\right)=cos\left(\frac{x-y}{2}\right)x+y=0\text{OR}\pm \left(\frac{x-y}{2}\right)=\frac{x+y}{2}$