If`sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"f i n d"(dy)/(dx)dot`

1.	If`sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"f i n d"(dy)/(dx)dot`
Answer» Let `t = tan theta` Then, `sinx = (2tan theta)/(1+tan^2theta)` As, `(2tan theta)/(1+tan^2theta) = sin2theta`, `=> sin x = sin2theta` `=> x= 2npi+2theta` `=>dx/ (d theta) = 2 ` Now, `tan y = (2tan theta)/(1-tan^2theta)` As, `(2tan theta)/(1- tan^2theta) = tan2theta`, `:. tany = tan2 theta` `=> y = npi+2theta` `=>dy/(d theta) = 2` `:. dy/dx = (dy/(d theta) )/(dx/(d theta) ) = 2/2 = 1` `:. dy/dx = 1`

Discussion

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