Evaluate the following:cosec-1(cosec \(\frac{13\pi}6\))

1.	Evaluate the following:cosec-1(cosec \(\frac{13\pi}6\))
Answer» The value of cosec\((\frac{13\pi}6)\) is 2. ∴ The question becomes cosec^–1(2) Let, cosec^–1(2) = y ∴ cosec y = 2 ⇒ cosec\((\frac{\pi}6)\) = 2 The range of principal value of cosec^–1 is \([\frac{-\pi}2,\frac{\pi}2]\)- {0} and cosec\((\frac{\pi}6)\) = 2 Therefore, the value of cosec^-1(cosec\((\frac{13\pi}6)\)) is \(\frac{\pi}6.\)

Answer»

The value of cosec\((\frac{13\pi}6)\) is 2.

∴ The question becomes cosec^–1(2)

Let, cosec^–1(2) = y

∴ cosec y = 2

⇒ cosec\((\frac{\pi}6)\) = 2

The range of principal value of cosec^–1 is \([\frac{-\pi}2,\frac{\pi}2]\)- {0} and

cosec\((\frac{\pi}6)\) = 2

Therefore, the value of cosec^-1(cosec\((\frac{13\pi}6)\)) is \(\frac{\pi}6.\)

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