If tan -1 x -tan -1 y -2 -7- then the value of -1 x - -1 y isA- 5 -B- 7-D- 2 -2

The correct option is B π7 nbsp; nbsp;tan^ 1x+tan^ 1y= 2π7 ⋯(1) Let ^ 1x+^ 1y=m ⋯(2) Adding (1) and (2), tan^ 1x+^ 1x+tan^ 1y+^ 1y=2π7+m ⇒ 2 ×π2=2π ...

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Byju's Answer

Standard XII

Mathematics

Logarithmic Differentiation

If tan -1 x +...

Question

If ${tan}^{- 1} x + {tan}^{- 1} y = \frac{2 π}{7},$ then the value of ${cot}^{- 1} x + {cot}^{- 1} y$ is

\frac{π}{7}

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\frac{π}{2}

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\frac{2 π}{7}

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\frac{5 π}{7}

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Solution

The correct option is A $\frac{π}{7}$
${tan}^{- 1} x + {tan}^{- 1} y = \frac{2 π}{7} \dots (1)$
$Let {cot}^{- 1} x + {cot}^{- 1} y = m \dots (2)$
Adding $(1)$ and $(2),$
${tan}^{- 1} x + {cot}^{- 1} x + {tan}^{- 1} y + {cot}^{- 1} y = \frac{2 π}{7} + m$
$\Rightarrow 2 \times \frac{π}{2} = \frac{2 π}{7} + m$
$\Rightarrow m = \frac{5 π}{7}$

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If tan−1x+tan−1y=2π7, then the value of cot−1x+cot−1y is

The correct option is A π7 tan−1x+tan−1y=2π7 ⋯(1) Let cot−1x+cot−1y=m ⋯(2) Adding (1) and (2), tan−1x+cot−1x+tan−1y+cot−1y=2π7+m ⇒2×π2=2π7+m ⇒m=5π7

If ${tan}^{- 1} x + {tan}^{- 1} y = \frac{2 π}{7},$ then the value of ${cot}^{- 1} x + {cot}^{- 1} y$ is