If tan -1 x-tan -1 y-4 -5- then -1 x- -1 y is equal toA- -B- 2 -5- 3 -5D-

The correct option is D π/5Given that nbsp;tan^ 1x+tan^ 1y=4π/5.....(1) Let ^ 1x+^ 1y = p.....(2) we know that tan^ 1a+^ 1a=π/2 Adding (1) and (2) tan^ 1x+^ ...

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Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

If tan -1 x+t...

Question

$If {tan}^{- 1} x + {tan}^{- 1} y = \frac{4 π}{5}, then {cot}^{- 1} x + {cot}^{- 1} y$ $is equal to$

π

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\frac{π}{5}

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\frac{2 π}{5}

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\frac{3 π}{5}

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Solution

The correct option is B $\frac{π}{5}$
Given that ${tan}^{- 1} x + {tan}^{- 1} y = \frac{4 π}{5}$ .....(1)
Let ${cot}^{- 1} x + {cot}^{- 1} y = p$ .....(2)
we know that ${tan}^{- 1} a + {cot}^{- 1} a = \frac{π}{2}$

Adding (1) and (2)
${tan}^{- 1} x + {cot}^{- 1} x + {tan}^{- 1} y + {cot}^{- 1} y = \frac{4 π}{5} + p$
$\Rightarrow \frac{π}{2} + \frac{π}{2} = \frac{4 π}{5} + p$
$\Rightarrow p = \frac{π}{5}$

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If tan−1x+tan−1y=4π5, then cot−1x+cot−1y is equal to

The correct option is B π5Given that tan−1x+tan−1y=4π5.....(1) Let cot−1x+cot−1y=p.....(2) we know that tan−1a+cot−1a=π2 Adding (1) and (2) tan−1x+cot−1x+tan−1y+cot−1y=4π5+p ⇒π2+π2=4π5+p ⇒p=π5

$If {tan}^{- 1} x + {tan}^{- 1} y = \frac{4 π}{5}, then {cot}^{- 1} x + {cot}^{- 1} y$ $is equal to$