Find the value of tan-1tan2-3-

We have to find the value of #160; #160; tan^ 1(tan2π3) tan^ 1(tan2π3) =tan^ 1(tan(π π3)) tan^ 1(tan2π3) =tan^ 1(tan( π3)) tan ...

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Circular Measurement of Angle

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Question

Find the value of ${tan}^{- 1} (tan \frac{2 π}{3})$ .

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Solution

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{tan}^{- 1} (tan 2 π / 3)

{tan}^{- 1} (tan \frac{2 π}{3})

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{cos}^{- 1} (cos \frac{7 π}{6})

{tan}^{- 1} (tan \frac{2 π}{3})

cos ({cos}^{- 1} (\frac{\sqrt{3}}{2}) + \frac{π}{6})

s i n^{- 1} (s i n \frac{2 π}{3}) = \frac{2 π}{3}

t a n^{- 1} (t a n \frac{2 π}{3}) = \frac{- π}{3}

c o s^{- 1} (c o s \frac{2 π}{3}) = \frac{2 π}{3}

s e c^{- 1} (s e c \frac{5 π}{4}) = \frac{3 π}{4}

s i n^{- 1} (s i n \frac{2 π}{3}) = \frac{2 π}{3}

t a n^{- 1} (t a n \frac{2 π}{3}) = \frac{- π}{3}

c o s^{- 1} (c o s \frac{2 π}{3}) = \frac{2 π}{3}

s e c^{- 1} (s e c \frac{5 π}{4}) = \frac{3 π}{4}

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