Evaluate:cot-1(cot \(\frac{19\pi}6\))

1.	Evaluate:cot-1(cot \(\frac{19\pi}6\))
Answer» The value of cot \(\frac{19\pi}6\) is √3. ∴ The question becomes cot^–1(√3). Let cot^–1(√3) = y ⇒ cot y = √3 = cot\(\frac{\pi}6\) = √3 The range of principal value of cot^–1is (0, π) and cot\(\frac{\pi}6\)= √3 ∴ The principal value of cot^–1(cot\(\frac{19\pi}6\) ) is \(\frac{\pi}6\).

Answer»

The value of cot \(\frac{19\pi}6\) is √3.

∴ The question becomes cot^–1(√3).

Let cot^–1(√3) = y

⇒ cot y = √3

= cot\(\frac{\pi}6\) = √3

The range of principal value of cot^–1is (0, π)

and cot\(\frac{\pi}6\)= √3

∴ The principal value of cot^–1(cot\(\frac{19\pi}6\) ) is \(\frac{\pi}6\).

Discussion