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Find the Values Of `Cos^(-1) (Cos (7pi)/6)` Is Equal to - Mathematics

Find the values of  `cos^(-1) (cos  (7pi)/6)` is equal to 

(A)  `(7pi)/6`

(B) `(5pi)/6`

(C) `pi/3`

(D) `pi/6`

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Solution

We know that cos−1 (cos x) = x if x in `[0, pi]`, which is the principal value branch of cos −1x.

Here `(7pi)/6 !in x in [0, pi]`

Now `cos^(-1) (cos  (7pi)/6)` can be written as

cos-1cos7π6 = cos-1cosπ+π6cos-1cos7π6 = cos-1- cosπ6             as, cosπ+θ = - cos θcos-1cos7π6  = cos-1- cosπ-5π6cos-1cos7π6 = cos-1-- cos 5π6   as, cosπ-θ = - cos θ

`:. cos^(-1) (cos  (7pi)/6) = cos^(-1) (cos  (5pi)/6) = (5pi)/6`

The correct answer is B.

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APPEARS IN

NCERT Class 12 Maths
Chapter 2 Inverse Trigonometric Functions
Q 19 | Page 48
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