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The value of cos ^-1(cos (7π)/(6)) is Single correct option
The value of
cos − 1 ( cos 7 π 6 ) \cos^{-1}\left(\cos\dfrac{7\pi}6\right) cos − 1 ( cos 6 7 π ) is
A. 7 π 6 \dfrac{7\pi}6 6 7 π B. π 6 \dfrac\pi6 6 π C. 2 π 3 \dfrac{2\pi}3 3 2 π D. 5 π 6 \dfrac{5\pi}6 6 5 π Show answer and solution Answer: (D) 5 π 6 \dfrac{5\pi}6 6 5 π
The principal value of
cos − 1 \cos^{-1} cos − 1 lies in
[ 0 , π ] [0,\pi] [ 0 , π ] . Since
cos 7 π 6 = − 3 2 = cos 5 π 6 \cos\dfrac{7\pi}6=-\dfrac{\sqrt3}2=\cos\dfrac{5\pi}6 cos 6 7 π = − 2 3 = cos 6 5 π and
5 π 6 ∈ [ 0 , π ] \dfrac{5\pi}6\in[0,\pi] 6 5 π ∈ [ 0 , π ] , the answer is
5 π 6 \dfrac{5\pi}6 6 5 π . The value
7 π 6 \dfrac{7\pi}6 6 7 π lies outside the principal range.
Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake