Find the principal value of cot−1(3−1)

Let y=cot−1(3−1)3−1=coty⇒ coty =3−1=−cot(3π)coty=cot(π−3π)cot y=cot(32π)∴ y=22πϵ 32πϵ (0;π)

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Find the principal value of ^{-1} ( {-1}{{3}} )

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Find the principal value of $cot^{- 1} (\frac{- 1}{3})$

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Find the principal value of

cot^{- 1} (\frac{- 1}{3})

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Let

y = cot^{- 1} (\frac{- 1}{3})

\frac{- 1}{3} = cot y \Rightarrow cot y = \frac{- 1}{3} = - cot (\frac{π}{3})

cot y = cot (π - \frac{π}{3})

cot y = cot (\frac{2 π}{3})

∴ y = \frac{2 π}{2} ϵ \frac{2 π}{3} ϵ (0; π)

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Question Text	Find the principal value of $cot^{- 1} (\frac{- 1}{3})$
Answer Type	Text solution:1
Upvotes	150