The value of sin(2 tan⁻¹(1/3)) + cos(tan⁻¹(2√2)) is:

The value of sin(2 tan⁻¹(1/3)) + cos(tan⁻¹(2√2)) is:

• A. 3/5 + 1/3
• B. 3/5 − 1/3
• C. 14/15
• D. 4/15

Answer: C) 14/15

Explanation: Let θ = tan⁻¹(1/3). sin 2θ = 2tanθ/(1+tan²θ) = 2(1/3)/(1+1/9) = (2/3)/(10/9) = 3/5. Let φ = tan⁻¹(2√2). cos φ = 1/√(1+8) = 1/3. Sum = 3/5 + 1/3 = 14/15.