What is the value of tan⁻¹(1/3) + tan⁻¹(1/2)?

• A) π/2
• B) π/3
• C) π/4
• D) tan⁻¹(1/3) + 2

To find the value of tan⁻¹(1/3) + tan⁻¹(1/2), we can use the formula for the sum of inverse tangents:

Sum of Inverse Tangents Formula

The formula states:

• tan⁻¹(a) + tan⁻¹(b) = tan⁻¹((a + b) / (1 - ab)) if ab < 1

Applying the Formula

In this case, let:

• a = 1/3
• b = 1/2

Now, calculate:

• ab = (1/3) * (1/2) = 1/6
• a + b = 1/3 + 1/2 = 5/6

Since ab < 1, we can apply the formula:

tan⁻¹(1/3) + tan⁻¹(1/2) = tan⁻¹((5/6) / (1 - 1/6)) = tan⁻¹((5/6) / (5/6)) = tan⁻¹(1)

Final Result

Since tan⁻¹(1) equals π/4, the answer is:

π/4