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{ ^{ -1 }( 3/5 ) } + { ^{ -1 }( 1/4 ) } =

Question

$tan^{- 1} (3/5) + tan^{- 1} (1/4) =$

0

π /4

3 n /4

None of these

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tan^{- 1} (3/5) + tan^{- 1} (1/4) =

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Text solutionVerified

given,

tan^{- 1} \frac{3}{5} + tan^{- 1} \frac{1}{4}

= tan^{- 1} (\frac{\frac{3}{5} + \frac{1}{4}}{1 - \frac{3}{5} \times \frac{1}{4}})

= tan^{- 1} (\frac{\frac{12 + 5}{20}}{1 - \frac{3}{20}})

= tan^{- 1} (\frac{\frac{17}{20}}{\frac{20 - 3}{20}})

= tan^{- 1} (\frac{\frac{17}{20}}{\frac{17}{20}})

= tan^{- 1} (1)

= \frac{π}{4}

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