The principal value of tan - 1 c o t 43 π 4 is, π 4, - π 4, 3 π 4, - 3 π 4

- π 2 tan - 1 x π 2 c o t 4 3 π 4 = c o t 1 0 π + 3 π 4 = c o t 3 π 4 = - 1 tan - 1 c o t 4 3 π 4 = tan - 1 - 1 = - π 4

The principal value of tan - 1 c o t 43 π 4 is

Question: Answered & Verified by Expert

The principal value of

\tan^{- 1} (c o t \frac{43 π}{4})

MathematicsInverse Trigonometric FunctionsJEE MainJEE Main 2014 (19 Apr Online)

Options:

Solution:

1070 Upvotes Verified Answer

The correct answer is:

- \frac{π}{4}

$\frac{- π}{2} < \tan^{- 1} x < \frac{π}{2}$

$c o t (\frac{43 π}{4}) = c o t (10 π + \frac{3 π}{4})$

$= c o t \frac{3 π}{4}$

$= - 1$

$\tan^{- 1} c o t (\frac{43 π}{4}) = \tan^{- 1} (- 1)$

$= - \frac{π}{4}$

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