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Find the dy/dx when sin x = (2t)/(1+...

Find the dy/dx when
` sin x = (2t)/(1+t^2), tan y = (2t)/(1-t^2)`

Text Solution

Verified by Experts

`sin x = (2t)/(1+t^2)` and `tan y = (2t)/(1-t^2)`
`implies x = sin^(-1) frac (2t)(1+t^2) = 2tan^(-1)t
and y = tan^(-1) frac (2t)(1-t^2) = 2 tan^(-1)t
implies y = x
dy/dx = 1`
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