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If $\cot^{- 1} x + \cot^{- 1} y + \cot^{- 1} z = \frac{π}{2},$ then $x + y + z$ is also equal to

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Correct option is C

cot−1x+cot−1y+cot−1z=π2,⇒π2−tan−1x+π2−tan−1y+π2−tan−1z=π2⇒tan(tan−1x+tan−1y+tan−1z)=tanπ⇒tanx+y+z−xyz1−(xy+yz+zx)=0⇒x+y+z=xyz

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If cot−1x+cot−1y+cot−1z=π2,then x+y+zis also equal to

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Ready to Test Your Skills?

free study material

If $\cot^{- 1} x + \cot^{- 1} y + \cot^{- 1} z = \frac{π}{2},$ then $x + y + z$ is also equal to