InterviewSolution
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InterviewSolution
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Solve :`cos^(-1)(1/2x^2+sqrt(1-x^2)1=(x^2)/4)=cos^(-1)x/2-cos^(-1)xdot` |
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Answer» `cos^(-1) ((1)/(2) x^(2) + sqrt(1 -x^(2)) sqrt(1 - (x^(2))/(4))) = cos^(-1) (x.(x)/(2) + sqrt(1 -x^(2)) sqrt(1 - ((x)/(2))^(2)))` for `cos^(-1) ((1)/(2) x^(2) + sqrt(1 - x^(2)) sqrt(1 - (x^(2))/(4))) = cos^(-1) (x)/(2) - cos^(-1) x` L.H.S. `gt 0`, hence R.H.S. `gt 0` `rArr cos^(-1).(x)/(2) - cos^(-1) gt 0 " or " cos^(-1).(x)/(2) gt cos^(-1) x` Since `cos^(-1) x` is a decreasing function, we get `(x)/(2) le x rArr (x)/(2) ge 0 rArr x ge 0 rArr x in [0,1]` |
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