The value of tan[cos⁻¹(4/5) + tan⁻¹(2/3)] is:

The value of tan[cos⁻¹(4/5) + tan⁻¹(2/3)] is:

• A. 6/17
• B. 7/6
• C. 17/6
• D. 6/7

Answer: C) 17/6

Explanation: Let α = cos⁻¹(4/5), so tan α = 3/4. Let β = tan⁻¹(2/3). tan(α+β) = (tanα+tanβ)/(1−tanα tanβ) = (3/4 + 2/3)/(1 − 3/4×2/3) = (17/12)/(1 − 6/12) = (17/12)/(6/12) = 17/6.