Question

What is the value of cos^-1(-x) for all x belongs to [-1, 1]?

(a) cos^-1(-x)

(b) π – cos^-1(x)

(c) π – cos^-1(-x)

(d) π + cos^-1(x)

I got this question in quiz.

My question comes from Inverse Trigonometry in chapter Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

Right choice is (b) π – cos^-1(x)

To explain: Let, θ = cos^-1(-x)

So, 0 ≤ θ ≤ π

=> -x = cosθ

=> x = -cosθ

=> x = cos(-θ)

Also, -π ≤ -θ ≤ 0

So, 0 ≤ π -θ ≤ π

=> -θ = cos^-1(x)

=> θ = -cos^-1(x)

So, cos^-1(x) = π – θ

θ = π – cos^-1(x)

=> cos^-1(-x) = π – cos^-1(x)