InterviewSolution
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InterviewSolution
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Differentiate `tan^(-1)((a cosx-b sinx)/(b cosx + a sinx))`w.r.t. x. |
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Answer» Let `y=tan^(-1)((acosx-bsinx)/(b cosx+asin x)).` Putting `a=r sin theta and b = r cos theta,` we get `y=tan^(-1){(r(sin thetacosx-cos thetasin x))/(r(cos thetacosx+sin thetasin x))}` `=tan^(-1){(sin(theta-x))/(cos(theta-x))}=tan^(-1){tan(theta-x)}` `=theta-x=(tan^(-1).(a)/(b)-x)[because (a)/(b)=tan theta rArr theta= tan^(-1).(1)/(b)].` `therefore(dy)/(dx)=(d)/(dx)(tan^(-1).(a)/(b)-x)` `=(d)/(dx)(tan^(-1).(a)/(b))-(d)/(dx)(x)=-1" "[because tan^(-1).(a)/(b)="constant"].` |
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