Inverse Trigonometric Functions

All trigonometric functions have inverse over their respective domains.

• True

• False

The value of expression ((cos^-1 x)^2) is equal to (sec^2 x).

• True

• False

The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.

• True

• False

The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.

• True

• False

The graph of inverse trigonometric can be obtained from the graph of their corresponding function by interchanging X and Y-axes.

• True

• False

The principal value of sin^-1 (cos (sin^-1 1/2)) is π/3.

• True

• False

The value of cot^-1 (-x) x ∈ ℝ in terms of cot^-1 x is π/2 - cot^-1 x.

• True

• False

The value of tan ((sin^-1 x + cos^-1 x)/2), when x = √3/2, is 1.

• True

• False

The value of cos (sin^-1 x + cos^-1 x), where |x| ≤ 1, is 1.

• True

• False

The values of cos^-1 (cos 14π/3) is -π/3.

• True

• False