If \tan(\frac{x + y}{x-y})=k, then \frac{dy}{dx} is equal ...

CBSE Class 12 Math 2023 All Sets Solved Paper

Question : 12 of 20

Marks: +1, -0

tan(\;{x + y}/{x-y})=k,

then

\;{dy}/{dx}

is equal to :

Solution:

\tan (\;{x+y}/{x-y}) =k

⇒ (\;{x+y}{x-y}) =\tan ^{-1}/{k}

⇒ \;{(x-y) (1+y^{'}) -(x+y) (1-y^{'}) }/{(x-y)^2}=0

⇒ x-y+x y^{'}-y y^{'}-x-y+x y^{'}+y y^{'}=0

⇒-2 y+2 x y^{'}=0

∴ \;{d y}/{d x}=\;{y}/{x}

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