If tan - 1-3 - - 1x - -2 then find the value of x-

We know that tan^ 1√(3)=π3 ∴ tan^ 1√(3)+^ 1x=π2 ⇒ π3+^ 1x=π2 ⇒ ^ 1x=π2 π3=3π 2π6=π6 ⇒ x=π6=√(3) ∴ x=√(3) ...

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Standard XII

Mathematics

Basic Trigonometric Identities

If tan - 1√...

Question

If ${tan}^{- 1} \sqrt{3} + {cot}^{- 1} x = \frac{π}{2}$ then find the value of $x$ .

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Solution

We know that ${tan}^{- 1} \sqrt{3} = \frac{π}{3}$

$∴ {tan}^{- 1} \sqrt{3} + {cot}^{- 1} x = \frac{π}{2}$

$\Rightarrow \frac{π}{3} + {cot}^{- 1} x = \frac{π}{2}$

$\Rightarrow {cot}^{- 1} x = \frac{π}{2} - \frac{π}{3} = \frac{3 π - 2 π}{6} = \frac{π}{6}$

$\Rightarrow x = cot \frac{π}{6} = \sqrt{3}$

$∴ x = \sqrt{3}$

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If tan−1√3+cot−1x=π2 then find the value of x.

We know that tan−1√3=π3∴tan−1√3+cot−1x=π2⇒π3+cot−1x=π2⇒cot−1x=π2−π3=3π−2π6=π6⇒x=cotπ6=√3∴x=√3

If ${tan}^{- 1} \sqrt{3} + {cot}^{- 1} x = \frac{π}{2}$ then find the value of $x$ .