What is the value of tan^(-1)(1) + tan^(-1)(2)?

What is the value of tan^(-1)(1) + tan^(-1)(2)?

Step 1: Identify the values for a and b. Here, a = 1 and b = 2.
Step 2: Use the formula for the sum of arctangents: tan^(-1)(a) + tan^(-1)(b) = tan^(-1)((a+b)/(1-ab)).
Step 3: Substitute a and b into the formula: tan^(-1)(1) + tan^(-1)(2) = tan^(-1)((1+2)/(1-1*2)).
Step 4: Calculate the numerator: 1 + 2 = 3.
Step 5: Calculate the denominator: 1 - (1*2) = 1 - 2 = -1.
Step 6: Now we have tan^(-1)(3/-1).
Step 7: Simplify tan^(-1)(3/-1) to tan^(-1)(-3).
Step 8: Recall that tan^(-1)(-x) = -tan^(-1)(x), so tan^(-1)(-3) = -tan^(-1)(3).
Step 9: Therefore, tan^(-1)(1) + tan^(-1)(2) = -tan^(-1)(3).
Step 10: Since tan^(-1)(3) is a positive angle, we can express this as π - tan^(-1)(3) to keep it in the range of arctangent.
Step 11: Finally, we know that tan^(-1)(1) = π/4, so we conclude that tan^(-1)(1) + tan^(-1)(2) = π/4.

No concepts available.