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{ ^{ - 1}}( {2 + 3 } ) =

Question

$cot^{- 1} (2 + 3) =$

A

\frac{π}{12}

B

\frac{π}{15}

C

\frac{π}{5}

D

\frac{3 π}{10}

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Text solutionVerified

Solution :- given

\Rightarrow co t^{- 1} (2 + 3)

\Rightarrow co t^{- 1} (\frac{2 ( 2 + 3 )}{2})

multiply num and den by 2

\Rightarrow co t^{- 1} (\frac{4 + 2 3}{3 - 1})

\Rightarrow co t^{- 1} (\frac{3 + 1 + 2 3}{( 3 ) ^{2} - ( 1 ) ^{2}})

\Rightarrow co t^{- 1} (\frac{( 3 ) ^{2} + ( 1 ) ^{2} + 2.1. 3}{( 3 + 1 ) ( 3 - 1 )})

\Rightarrow co t^{- 1} (\frac{( 3 + 1 ) ^{2}}{( 3 + 1 ) ( 3 - 1 )})

\Rightarrow co t^{- 1} (\frac{3 + 1}{3 - 1})

\Rightarrow co t^{- 1} (\frac{( co t 45 co t 30 + 1 )}{co t 30 - co t 45})

= co t^{- 1} (co t (45 - 30))

= 4 5^{\circ} - 3 0^{\circ}

= 1 5^{\circ}

= \frac{π}{12}

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Question Text	$cot^{- 1} (2 + 3) =$
Answer Type	Text solution:1
Upvotes	150