Using the formula tan^(-1)(a) + tan^(-1)(b) = tan^(-1)((a+b)/(1-ab)), we have tan^(-1)(1) + tan^(-1)(2) = tan^(-1)((1+2)/(1-1*2)) = tan^(-1)(3/-1) = π - tan^(-1)(3) = π/4.
Questions & Step-by-step Solutions
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Q
Q: What is the value of tan^(-1)(1) + tan^(-1)(2)?
Solution: Using the formula tan^(-1)(a) + tan^(-1)(b) = tan^(-1)((a+b)/(1-ab)), we have tan^(-1)(1) + tan^(-1)(2) = tan^(-1)((1+2)/(1-1*2)) = tan^(-1)(3/-1) = π - tan^(-1)(3) = π/4.
Steps: 11
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)).
