InterviewSolution
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InterviewSolution
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The number of ordered triplets `(x,y,z)` satisfy the equation `(sin^(- 1)x)^2=(pi^2)/4+(sec^(- 1)y)^2+(tan^(- 1)z)^2`A. 2B. 4C. 6D. 8 |
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Answer» Correct Answer - A `(sin^(-1)x)in[-(pi)/(2),(pi)/(2)]` `therefore (sin^(-1)x)^(2)le (pi^(2))/(4)` `(sec^(-1)y)^(2), (tan^(-1)z)^(2)ge 0` `therefore R.H.S. ge (pi^(2))/(4)` `therefore (sin^(-1)x)^(2)=(pi^(2))/(4)` `therefore (sex^(-1)y)^(2)+(tan^(-1)z)^(2)=0` or `sec^(-1)y=tan^(-1)z=0` `therefore sin^(-1)x = pm(pi)/(2), y = 1, z = 0` |
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