InterviewSolution
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InterviewSolution
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If `x = 3 cos theta - 2 cos^3 theta,y = 3 sin theta - 2 sin^3 theta`, then `dy/dx` is |
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Answer» Correct Answer - `cot theta` `"We have, "x=3 cos theta -2 cos^(3)theta` `"and "y=3 sin theta - 2 sin ^(3)theta` `therefore" "(dx)/(d""theta)=-3 sin theta -2xx3 cos^(2) theta(d)/(d""theta)(cos theta)` `=-3 sin theta + 6 cos^(2) theta sin theta` `"And "(dy)/(d""theta)=3cos theta -2xx3sin^(2)theta(d)/(d""theta)(sin theta)` `=3 cos theta -6 sin^(2) theta. cos theta` `"Now, "(dy)/(dx)=(dy//d""theta)/(dx//d""theta)=(3cos theta-6 sin^(2)theta cos theta)/(-3 sin theta + 6cos^(2) theta sin theta)` `=(3cos theta(1-2 sin^(2)theta))/(3 sin theta(-1+2cos^(2)theta))=cot theta. (cos 2theta)/(cos 2theta)=cot theta` |
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