If tan−1(tan45π)=α and tan−1(−tan32π)=β then.

tan−1(tan 45π )=α⇒45π =αAlso, tan−1(tan −32π )=β ⇒−32π =β ⇒α+β=45π −32π ⇒α+β=127π

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If ^{-1}({5}{4})= and ^{-1}( - {2}{3})= then.

Question

If $tan^{- 1} (tan \frac{5 π}{4}) = α$ and $tan^{- 1} (- tan \frac{2 π}{3}) = β$ then.

α - β = \frac{7 π}{12}

α + β = \frac{7 π}{12}

2 α + 3 β = \frac{7 π}{12}

4 α + 3 β = \frac{7 π}{12}

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Levi Discussed

tan^{- 1} (tan \frac{5 π}{4}) = α

and

tan^{- 1} (- tan \frac{2 π}{3}) = β

then.

8 mins ago

Discuss this question LIVE

8 mins ago

$tan^{- 1} (tan \frac{5 π}{4}) = α$

$\Rightarrow \frac{5 π}{4} = α$

Also, $tan^{- 1} (tan - \frac{2 π}{3}) = β$

$\Rightarrow - \frac{2 π}{3} = β$

$\Rightarrow α + β = \frac{5 π}{4} - \frac{2 π}{3}$

$\Rightarrow α + β = \frac{7 π}{12}$

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Question Text	If $tan^{- 1} (tan \frac{5 π}{4}) = α$ and $tan^{- 1} (- tan \frac{2 π}{3}) = β$ then.
Answer Type	Text solution:1
Upvotes	150