Find your own values that prove that tan(u-v) ≠ tan u - tan v. Show your work and explain why you chose these values.

Answer 1

Just pick some random values for u and v, like u = 45° and v = 30°

tan(45 - 30) = tan(15) and using my calculator tan(15) = 0.2679

and again using my calculator tan(45) - tan(30) = 1 - 0.5774 = 0.4226

Since 0.2679 ≠ 0.4226, tan(45 - 30) ≠ tan(45) - tan(30)

If you need to use exact values instead of calculator values, you'll need to use the difference identity for tangent to get the exact value of tan(15). Use the unit circle to get the exact for tan(45) and tan(30)