Given sin(u)= -7/25 and cos(v) = -4/5, what is the exact value of cos(u-v) if both angles are in quadrant 3

Given:

To find:

The exact value of cos(u-v) if both angles are in quadrant 3.

Solution:

In 3rd quadrant, cos and sin both trigonometric ratios are negative.

We have,

Now,

On further simplification, we get

Similarly,

Now,

Therefore, the value of cos (u-v) is 0.1872.

the third picture

step-by-step explanation: