The value of cos^-1(cos 5π/3) + sin^-1 (sin 5π/3) is A. π/2 B. 5π/3 C. 10π/3 D. 0

Question

The value of cos^-1(cos \(\frac{5\pi}3\)) + sin^-1 \(\frac{5\pi}3\)) is

A. \(\frac{\pi}2\)

B. \(\frac{5\pi}3\)

C. \(\frac{5\pi}3\)

D. 0

Answer 1

Correct option is D. 0

We need to find the value of:

Since, cos\((2\pi-\frac{\pi}3)\) lies on IV Quadrant and cosine is positive in IV Quadrant.

 cos\((2\pi-\frac{\pi}3)\)  = - sin\(\frac{\pi}3\)

And since, sin\((2\pi-\frac{\pi}3)\) lies on IV Quadrant and sine is negative in IV Quadrant.