The value of \(cos^{-1}\left(cos\frac{13\pi}{6}\right)\) isA. \(\f

1.	The value of \(cos^{-1}\left(cos\frac{13\pi}{6}\right)\) isA. \(\frac{13\pi}{6}\)B. \(\frac{7\pi}{6}\)C. \(\frac{5\pi}{6}\)D. \(\frac{\pi}{6}\)
Answer» Correct Answer is \(\frac{\pi}{6}\) Now, let x = \(cos^{-1}(cos\left(\frac{13\pi}{6}\right)\) ⇒ cos x =cos ( \(\frac{13\pi}{6}\)) Here ,range of principle value of cos is [0, π] ⇒ x = \(\frac{13\pi}{6}\)∉ [0, π] Hence for all values of x in range [0, π] ,the value of \(cos^{-1}(cos\left(\frac{13\pi}{6}\right)\)is ⇒ cos x =cos (2π - \(\frac{\pi}{6}\)) (\(\because\) cos ( \(\frac{13\pi}{6}\))= cos (2π - \(\frac{\pi}{6}\)) ) ⇒ cos x =cos ( \(\frac{\pi}{6}\)) ( \(\because\)cos (2π - θ)= cosθ) ⇒ x = \(\frac{\pi}{6}\)

The value of \(cos^{-1}\left(cos\frac{13\pi}{6}\right)\) isA. \(\frac{13\pi}{6}\)B. \(\frac{7\pi}{6}\)C. \(\frac{5\pi}{6}\)D. \(\frac{\pi}{6}\)

Answer»

Correct Answer is \(\frac{\pi}{6}\)

Now, let x = \(cos^{-1}(cos\left(\frac{13\pi}{6}\right)\)

⇒ cos x =cos ( \(\frac{13\pi}{6}\))

Here ,range of principle value of cos is [0, π]

⇒ x = \(\frac{13\pi}{6}\)∉ [0, π]

Hence for all values of x in range [0, π] ,the value of

\(cos^{-1}(cos\left(\frac{13\pi}{6}\right)\)is

⇒ cos x =cos (2π - \(\frac{\pi}{6}\)) (\(\because\) cos ( \(\frac{13\pi}{6}\))= cos (2π - \(\frac{\pi}{6}\)) )

⇒ cos x =cos ( \(\frac{\pi}{6}\)) ( \(\because\)cos (2π - θ)= cosθ)

⇒ x = \(\frac{\pi}{6}\)