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Find the value of tan-1(tan 5π6)+cos-1(cos 13π6) - Mathematics

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Question

Find the value of `tan^-1 (tan  (5pi)/6) +cos^-1(cos  (13pi)/6)`

Sum
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Solution

We know that `(5pi)/6 ∉ (- pi/2, pi/2)` and `(13pi)/6 ∉ [0, pi]`

∴ `tan^-1 (tan  (5pi)/6) + cos^1(cos  (13pi)/6)`

= `tan^-1 [tan (pi - pi/6)] + cos^-1[cos(2pi + pi/6)]`

= `tan^-1[tan(- pi/6)] + cos^-1(cos  pi/6)`

= `tan^-1 (tan  pi/6)+ cos^-1 (cos  pi/6)`

= `- tan^-1 (tan  pi/6) + cos^-1(cos  pi/6)`  .....[∵ tan–1(– x) = – tan– 1x]

= `- pi/6 + pi/6`

= 0

Hence, `tan^-1 (tan  (5pi)/6) +cos^-1(cos  (13pi)/6)` = 0

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Chapter 2: Inverse Trigonometric Functions - Exercise [Page 35]

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NCERT Exemplar Mathematics [English] Class 12
Chapter 2 Inverse Trigonometric Functions
Exercise | Q 1 | Page 35

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