InterviewSolution
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InterviewSolution
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यदि (If) `x=asin2t(1+cos2t)` तथा (and) `y=bcos2t(1-cos2t)`, दिखाएँ कि (show that ) `((dy)/(dx))_(t=(pi)/(4))=(b)/(a)` |
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Answer» यहाँ `x=asin2t(1+cos2t)` `rArr(dx)/(dt)=a.[2cos2t(1+cos2t)+sin2t(-2sin2t)]` `=2a[cos2t+cos^(2)2t-sin^(2)2t]` `=2a[cos2t+cos4t]` साथ ही `y=b cos2t(1-cos2t)` `rArr(dy)/(dt)=b[-2sin2t(1-cos2t)+cos2t.2sin2t]` `=2b[-sin2t+2sin2tcos2t]` `=2b[-sin2t+sin4t]` `therefore(dy)/(dx)=(dy//dt)/(dx//dt)=(2b[-sin2t+sin4t])/(2a[cos2t+cos4t])` `rArr((dy)/(dx))_(t=(pi)/(4))=(b)/(a)[(-"sin"(pi)/(2)+sinpi)/("cos"(pi)/(2)+"cos"pi)]=(b)/(a)[(-1+0)/(0-1)]=(b)/(a)`. |
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