Question

What will be the value of x + y + z if cos^-1 x + cos^-1 y + cos^-1 z = 3π?

(a) -1/3

(b) 1

(c) 3

(d) -3

I had been asked this question in homework.

My enquiry is from Inverse Trigonometry in chapter Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

Right answer is (d) -3

Easy explanation: The equation is cos^-1 x + cos^-1 y + cos^-1 z = 3π

This means cos^-1 x = π, cos^-1 y = π and cos^-1 z = π

This will be only possible when it is in maxima.

As, cos^-1 x = π so, x = cos^-1 π = -1    similarly, y = z = -1

Therefore, x + y + z = -1 -1 -1

So, x + y + z = -3.