InterviewSolution
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InterviewSolution
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If `x=a(cos theta+log tan(theta/2))` and `y=a sin theta` then find `(dy)/(dx)` at `theta=pi/3` and `theta=pi/4` |
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Answer» We have `x=a{cos theta +log tan(theta//2)}` `rArr(dx)/(d theta)=a{-sin theta+(sec^(2)(theta//2))/(2tan(theta//2))}=a{-sin theta+(1)/(2sin (theta//2)cos(theta//2))}` `=a{-sintheta+(1)/(sin theta)}=(a(1-sin^(2)theta))/(sintheta)=(acos^(2)theta)/(sin theta).` And, `y=a sin theta rArr (dy)/(dx)=a cos theta.` `therefore(dy)/(dx)=((dy)/(d theta)xx(d theta)/(dx))=(a cos theta.(sin theta)/(a cos^(2)theta))=tan theta.` `therefore[(dy)/(dx)]_(theta=pi//2)=tan.(pi)/(4)=1.` |
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