Question

Evaluate sec⁻¹ (-√2)

Answer 1

Answer:

Principal value of sec⁻¹ (-√2) is 3π/4

Step-by-step explanation:

we know that the range of principal value of $sec^{-1}x$ is  [0,π]-{π/2} .

Let sec⁻¹ (-√2) =θ.Then

sec θ = -√2

$- sec(\frac{\pi}{4}) = sec (\pi-\frac{\pi}{4} ) \\\\\\=sec (\frac{3\pi}{4} )$  

∴ θ = 3π/4 ∈ [0,π]-{π/2}

Hence,principal value of sec⁻¹ (-√2) is 3π/4.