Question

The probability that $si{n}^{-1}\left(sinx\right)+co{s}^{-1}\left(cosy\right)$ is an integer $x,y\in$ {1,2,3,4} is

• A. $\frac{1}{16}$
• B. $\frac{3}{16}$
• C. $\frac{15}{16}$
• D. $\frac{1}{17}$

Answer 1

The correct option is B $\frac{3}{16}$

$si{n}^{-1}\left(sinx\right)+co{s}^{-1}\left(cosy\right)$ to be integer $x\in [-\frac{\pi }{2}\frac{\pi }{2}]$ and $y\in [0,\pi ]\Rightarrow x=1$ and y =1,2,3. required Probability =$\frac{3}{16}$