One branch of cos–1 other than the principal value branch correspond

1.	One branch of cos–1 other than the principal value branch corresponds to(A) [π/2, 3π/2](B) [π, 2π] - {3π/2}(C) (0, π)(D) [2π, 3π]
Answer» (D) is the correct answer. We know that the principal value branch of cos^-1x is [0, π]. Also, we know that the period of cosθ is 2π. Now, let θ \(\in\) [2π, 3π] And cos(2π – θ) = cos θ Thus, 2π – θ \(\in\) [0, π]. Therefore, [2π, 3π] corresponds to the principal value branch for cos^-1x.

One branch of cos–1 other than the principal value branch corresponds to(A) [π/2, 3π/2](B) [π, 2π] - {3π/2}(C) (0, π)(D) [2π, 3π]

Answer»

(D) is the correct answer.

We know that the principal value branch of cos^-1x is [0, π].

Also, we know that the period of cosθ is 2π.

Now, let θ \(\in\) [2π, 3π]

And cos(2π – θ) = cos θ

Thus, 2π – θ \(\in\) [0, π].

Therefore, [2π, 3π] corresponds to the principal value branch for cos^-1x.