InterviewSolution
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InterviewSolution
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The number of real solutions of `tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+x+1)=pi/2`is`z`ero b. one``c. twod. infiniteA. zeroB. oneC. twoD. infinite |
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Answer» Correct Answer - C Given function is `tan^(-1)sqrt(x(x+1)) + sin ^(-1)sqrt(x^(2) + x + 1) = (pi)/(2)` Function is defined, if (i) `x (x + 1) ge 0`, since domain of square root function. (ii) `x^(2) + x + 1 ge 0`, since domain of square root function. (iii) ` sqrt(x^(2) + x + 1) le 1`, since domain of `sin ^(-1)` function. From (ii) and (iii)`, 0 le x^(2) + x + 1 le 1 nn x^(2) + x ge 0` `rArr " " 0 le x ^(2) + x + 1 le 1 nn x^(2) + x + 1 ge 1` `rArr " " x ^(2) + x + 1 = 1 ` `rArr " " x^(2) + x = 0` `rArr " " x(x+1) =0` `rArr " " x=0, x =-1` |
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