InterviewSolution
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InterviewSolution
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If `cos^(- 1)x-cos^(- 1)(y/2)=alpha` then `4x^2-4xycosalpha+y^2=`A. 4B. `2 sin^(2) alpha`C. `-4 sin^(2) alpha`D. `4 sin^(2) alpha` |
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Answer» Correct Answer - D We have `cos^(-1) x - cos^(-1).(y)/(2) = alpha` or `x = cos (cos^(-1).(y)/(2) + alpha)` `= cos (cos^(-1).(y)/(2)) cos alpha - sin (cos^(-1).(y)/(2)) sin alpha` `= (y)/(2) cos alpha - sqrt(1 - (y^(2))/(4)) sin alpha` or `2x = y cos alpha - sin alpha sqrt(4 -y^(2))` or `2x - y cos alpha = - sin alpha sqrt(4 -y^(2))` Squaring, we get `4x^(2) + y^(2) cos^(2) alpha - 4xy cos alpha = 4 sin^(2) alpha - y^(2) sin^(2) alpha` or `4x^(2) - 4xy cos alpha + y^(2) = 4 sin^(2) alpha` |
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