If fx-y-cos-11-xy-1-x2-1-y2- then fx-

The correct option is B 1/1+x^2 Let x=tanA and y=tanB Then, f(x,y)=cos^ 1(1 tanAtanBsecAsecB) #160; #160; #160; #160; #160; ...

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Standard XII

Mathematics

Variable Separable Method

If fx,y=cos...

Question

If $f (x, y) = {cos}^{- 1} {\frac{1 - x y}{\sqrt{1 + x^{2}} \sqrt{1 + y^{2}}}}$ , then $f_{x} =$

\frac{1}{1 + y^{2}}

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\frac{1}{1 + x^{2}}

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\frac{1 + y^{2}}{1 + x^{2}}

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\frac{- 1}{1 + x^{2}}

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Solution

The correct option is B $\frac{1}{1 + x^{2}}$
Let $x = t a n A$ and $y = t a n B$
Then, $f (x, y) = c o s^{- 1} (\frac{1 - t a n A t a n B}{s e c A s e c B})$

$= c o s^{- 1} (c o s (A + B))$

$= A + B$

$= t a n^{- 1} x + t a n^{- 1} y$

Now, $f_{x} = \frac{d}{d x} (t a n^{- 1} x) = \frac{1}{1 + x^{2}}$

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