Evaluate the following:sec-1(sec \(\frac{9\pi}5\))

1.	Evaluate the following:sec-1(sec \(\frac{9\pi}5\))
Answer» sec\((\frac{9\pi}5)\) can be written as sec\((2\pi-\frac{\pi}5)\) Also, we know sec(2π - θ) = sec(θ) ∴ sec \((2\pi-\frac{\pi}5)\) = sec \((\frac \pi 5)\) ∴ Now the given equation can be written as sec^–1sec\((\frac \pi 5)\) As sec^-1(sec x) = x Provided x ∈ [0,π] - \(\{\frac \pi 2\}\) ∴ we can write sec^-1sec\((\frac{\pi}5)\) as \(\frac{\pi}5.\)

Answer»

sec\((\frac{9\pi}5)\) can be written as sec\((2\pi-\frac{\pi}5)\)

Also, we know sec(2π - θ) = sec(θ)

∴ sec \((2\pi-\frac{\pi}5)\) = sec \((\frac \pi 5)\)

∴ Now the given equation can be written as sec^–1sec\((\frac \pi 5)\)

As sec^-1(sec x) = x

Provided x ∈ [0,π] - \(\{\frac \pi 2\}\)

∴ we can write sec^-1sec\((\frac{\pi}5)\) as \(\frac{\pi}5.\)

Discussion