InterviewSolution
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InterviewSolution
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If `y="tan"^(-1)((sqrt(1+sinx)+sqrt(1-sinx)))/((sqrt(1+sinx)-sqrt(1-sinx)))," find "(dy)/(dx).` |
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Answer» We have `y=tan^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))xx(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)+sqrt(1-sinx))}` `=tan^(-1){((1+sinx)+(1-sinx)+2sqrt(1-sin^(2)x))/((1+sinx)-(1-sinx))}=tan^(-1)((1+cosx)/(sinx))` `=tan^(-1){(2cos^(2)(x//2))/(2sin(x//2)cos(x//2))}=tan^(-1){"cot"(x)/(2)}=tan^(-1){tan((pi)/(2)-(x)/(2))}` `=((pi)/(2)-(x)/(2)).` `therefore(dy)/(dx)=(d)/(dx)((pi)/(2)-(x)/(2))=(d)/(dx)((pi)/(2))-(d)/(dx)((x)/(2))=(0-(1)/(2))=-(1)/(2).` |
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