If -1-1-x2-cosec-1-1-y2-4- -11-2-then x-y-z is equal to

The correct option is D xyzsec^ 1√(1 x^2)+cosec^ 1√(1+y^2)/4+cot^ 11/z=π ⇒ tan^ 1x+tan^ 1y+tan^ 1z=π ⇒ tan^ 1(x+y+z xyz/1 xy yz zx )=π ⇒ x+y+z=xyz ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

If -1√1-x2+co...

Question

If $s e c^{- 1} \sqrt{1 - x^{2}} + c o s e c^{- 1} \frac{\sqrt{1 + y^{2}}}{4} + c o t^{- 1} \frac{1}{z} = π$ ,then x+y+z is equal to

xyz

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2xyz

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xyz²

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x²yz

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Solution

The correct option is A
xyz

$s e c^{- 1} \sqrt{1 - x^{2}} + c o s e c^{- 1} \frac{\sqrt{1 + y^{2}}}{4} + c o t^{- 1} \frac{1}{z} = π$
$\Rightarrow t a n^{- 1} x + t a n^{- 1} y + t a n^{- 1} z = π$
$\Rightarrow t a n^{- 1} (\frac{x + y + z - x y z}{1 - x y - y z - z x}) = π$
$\Rightarrow x + y + z = x y z$

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Similar questions

Q. If

{sec}^{- 1} \sqrt{1 + x^{2}} + {cosec}^{- 1} (\frac{\sqrt{1 + y^{2}}}{y}) + {cot}^{- 1} (\frac{1}{z}) = π

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Q. If

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If sec−1√1−x2+cosec−1√1+y24+cot−11z=π ,then x+y+z is equal to

The correct option is A xyzsec−1√1−x2+cosec−1√1+y24+cot−11z=π ⇒tan−1x+tan−1y+tan−1z=π ⇒tan−1(x+y+z−xyz1−xy−yz−zx)=π ⇒x+y+z=xyz

If $s e c^{- 1} \sqrt{1 - x^{2}} + c o s e c^{- 1} \frac{\sqrt{1 + y^{2}}}{4} + c o t^{- 1} \frac{1}{z} = π$ ,then x+y+z is equal to