InterviewSolution
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InterviewSolution
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यदि `y=sqrt((1-sin2x)/(1+sin2x))`, तो सिद्ध कीजिए कि `(dy)/(dx)+sec^(2)((pi)/(4)-x)=0.` |
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Answer» `y=sqrt((1-sin2x)/(1+sin2x))` `=sqrt((cos^(2)x+sin^(2)x-2sin x cosx)/(cos^(2)x+sin^(2)x+2sin x cos x))` `=sqrt(((cosx-sinx)^(2))/((cosx+sinx)^(2)))=(cosx-sinx)/(cosx+sinx)` `=(1-tanx)/(1+tanx)=(tan.(pi)/(4)-tanx)/(1+tan.(pi)/(4).tanx)` `=tan((pi)/(4)-x)` `rArr" "(dy)/(dx)=(d)/(dx)tan((pi)/(4)-x)` `=sec^(2)((pi)/(4)-x)(d)/(dx)((pi)/(4)-x)` `=-sec^(2)((pi)/(4)-x)` `rArr" "(dy)/(dx)+sec^(2)((pi)/(4)-x)=0` यही सिद्ध करना था । |
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