# DOMAIN AND RANGE OF INVERSE TRIG FUNCTIONS

Problem 1 :

Domain of the function sin-1 x is ....

Solution:

Consider the given function as,

y = sin-1 x

The graph of sin-1 x or arc sin x is given as

-π/2 ≤ sin-1x ≤ π/2

-1 ≤ sin-1x ≤ 1

Hence, the domain of the function is [-1, 1].

Problem 2 :

Range of the function cos-1x is ....

Solution:

Range of the function cos-1x is [0, π].

Problem 3 :

The principal value of tan-1√3 is .....

Solution:

Let y = tan-1(√3)

tan y = √3

We know that the range of the principal value branch of tan-1(-π/2, π/2).

tan y = tan(π/3)

y = π/3

Hence, the principal value of tan-1(√3) is π/3.

Problem 4 :

Solution:

Problem 5 :

Principal values of the function tan-1x lie in the interval....

Solution:

We know that range of principal value of tan-1x is (-π/2, π/2).

Problem 6 :

Solution:

Problem 7 :

Solution:

Problem 8 :

Solution:

Problem 9 :

Solution:

Domain of sec-1(1/2) is R - (-1, 1).

(i.e) (-∞, -1] ∪ [1, ∞)

So, no set of values exist for sec-1(1/2).

Problem 10 :

For x ∈ R, tan-1(x2 + 1) + cot-1(x2 + 1) is equal to ....

Solution:

Problem 11 :

If cos-1(-x) = α - cos-1x, then the value of α is ....

Solution:

We know that cos-1(-x) = π - cos-1x

By comparing, we get α = π

Hence, α = π.

Problem 12 :

Solution:

Given, |x| ≥ √2

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