Find the value of tan -1-1-3- -11-3-tan -1-sin-2-

We have, tan^ 1 ( 1/√(3) )+cot^ 1 ( 1/√(3) )+tan^ 1 [ sin ( π/2 ) ] =tan^ 1 ( tan5π/6 )+cot^ 1(cotπ/3 )+tan^ 1( 1) =tan^ 1 [ tan(π π/6 ) ]+cot^ 1 [ cot ( ...

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Byju's Answer

Standard XII

Mathematics

Standard Formulae - 3

Find the valu...

Question

Find the value of $t a n^{- 1} (- \frac{1}{\sqrt{3}}) + c o t^{- 1} (\frac{1}{\sqrt{3}}) + t a n^{- 1} [s i n (\frac{- π}{2})] .$

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Solution

We have, $t a n^{- 1} (- \frac{1}{\sqrt{3}}) + c o t^{- 1} (\frac{1}{\sqrt{3}}) + t a n^{- 1} [s i n (\frac{- π}{2})] = t a n^{- 1} (t a n \frac{5 π}{6}) + c o t^{- 1} (c o t \frac{π}{3}) + t a n^{- 1} (- 1) = t a n^{- 1} [t a n (π - \frac{π}{6})] + c o t^{- 1} [c o t (\frac{π}{3})] + t a n^{- 1} [t a n (π - \frac{π}{4})] = t a n^{- 1} (- t a n \frac{π}{6}) + c o t^{- 1} (c o t \frac{π}{3}) + t a n^{- 1} (- t a n \frac{π}{4})$

$⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} ∵ t a n^{- 1} (t a n x) = x, x \in (- \frac{π}{2} \frac{π}{2}), c o t^{- 1} (c o t x) = x, x \in (0, π) a n d t a n^{- 1} (- x) = - t a n^{- 1} x \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$

$= - \frac{π}{6} + \frac{π}{3} - \frac{π}{4} = \frac{- 2 π + 4 π - 3 π}{12} = \frac{- 5 π + 4 π}{12} = - \frac{π}{12}$

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Similar questions

Q. Find the value of

tan [{sin}^{- 1} (\frac{1}{\sqrt{2}}) + cos ({sin}^{- 1} (\frac{1}{2}) + {tan}^{- 1} (\sqrt{3}))] - cos e c ({tan}^{- 1} \frac{4}{3})

Q. The value of

({tan}^{- 1} π + {tan}^{- 1} (\frac{1}{π})) + {tan}^{- 1} \sqrt{3} - {sec}^{- 1} (- 2)

is equal to

Inverse circular functions,Principal values of

{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

(a)

{t a n}^{- 1} \frac{1}{2} + {t a n}^{- 1} \frac{1}{3} = \frac{π}{4}

(b)

{t a n}^{- 1} \frac{1}{2} + {t a n}^{- 1} \frac{1}{5} + {t a n}^{- 1} \frac{1}{8} = \frac{π}{4}

(c)

{t a n}^{- 1} \frac{3}{4} + {t a n}^{- 1} \frac{3}{5} - {t a n}^{- 1} \frac{8}{19} = \frac{π}{4}

Inverse circular functions,Principal values of ${sin}^{- 1} x, {c o s}^{- 1} x, {tan}^{- 1} x$ .
${tan}^{- 1} x + {tan}^{- 1} y = {tan}^{- 1} \frac{x + y}{1 - x y}$ , $x y < 1$
$π + {tan}^{- 1} \frac{x + y}{1 - x y}$ , $x y > 1$ .
Evaluate the following :
(a) $sin [\frac{π}{3} - {sin}^{- 1} (- \frac{1}{2})]$
(b) $sin [\frac{π}{2} - {sin}^{- 1} (- \frac{\sqrt{3}}{2})]$

Q. Consider the following :
1.

{sin}^{- 1} \frac{4}{5} + {sin}^{- 1} \frac{3}{5} = \frac{π}{2}

{tan}^{- 1} \sqrt{3} + {tan}^{- 1} 1 = - {tan}^{- 1} (2 + \sqrt{3})

Which of the above is/are correct?

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Find the value of tan−1(−1√3)+cot−1(1√3)+tan−1[sin(−π2)].

Find the value of $t a n^{- 1} (- \frac{1}{\sqrt{3}}) + c o t^{- 1} (\frac{1}{\sqrt{3}}) + t a n^{- 1} [s i n (\frac{- π}{2})] .$