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The probability that sin -1 (sin x)+cos -1 (cos y) is an integer for x,y belongs to {1,2,3,4} is

The probability that sin-1 (sin x)+cos-1 (cos y) is an integer for x,y belongs to {1,2,3,4} is

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

sin^{-1}sinx = x
When
\frac{-\pi }{2}\leq x\leq \frac{\pi }{2}
cos^{-1}cosy = y
When
0\leq y\leq \pi
Out of total 16 combination of {x, y}, only one combination {1,1} is possible
Probability:
\frac{1}{16}

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