Find the value of the following-tan -1tan7 -6

Tan^ 1 ( tan7π/6 )=tan^ 1 [ tan ( π+π/6 ) ]; where π/6ϵ ( π/2,π/2 ) (principal interval) ∴ tan^ 1 ( tan7π/6 )=tan^ 1 [ tanπ/6 ]=π/6 [∵ tan(π+θ)=tanθ] ...

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Byju's Answer

Standard XII

Mathematics

General Solution of Trigonometric Equation

Find the valu...

Question

Find the value of the following:

$t a n^{- 1} (t a n \frac{7 π}{6})$

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Solution

$t a n^{- 1} (t a n \frac{7 π}{6}) = t a n^{- 1} [t a n (π + \frac{π}{6})]; w h e r e \frac{π}{6} ϵ (- \frac{π}{2}, \frac{π}{2})$ (principal interval)
$∴ t a n^{- 1} (t a n \frac{7 π}{6}) = t a n^{- 1} [t a n \frac{π}{6}] = \frac{π}{6} [∵ t a n (π + θ) = t a n θ]$

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Find the value of the following: tan−1(tan7π6)

tan−1(tan7π6)=tan−1[tan(π+π6)];whereπ6ϵ(−π2,π2) (principal interval) ∴ tan−1(tan7π6)=tan−1[tanπ6]=π6 [∵tan(π+θ)=tanθ]

Find the value of the following:

$t a n^{- 1} (t a n \frac{7 π}{6})$

$t a n^{- 1} (t a n \frac{7 π}{6}) = t a n^{- 1} [t a n (π + \frac{π}{6})]; w h e r e \frac{π}{6} ϵ (- \frac{π}{2}, \frac{π}{2})$ (principal interval)
$∴ t a n^{- 1} (t a n \frac{7 π}{6}) = t a n^{- 1} [t a n \frac{π}{6}] = \frac{π}{6} [∵ t a n (π + θ) = t a n θ]$