Evaluate tan^(-1)(1) + tan^(-1)(√3).

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Question: Evaluate tan^(-1)(1) + tan^(-1)(√3).

Options:

Correct Answer: π/2

Solution:

tan^(-1)(1) = π/4 and tan^(-1)(√3) = π/3. Therefore, π/4 + π/3 = π/2.

Evaluate tan^(-1)(1) + tan^(-1)(√3).

Evaluate tan^(-1)(1) + tan^(-1)(√3).

Step 1: Understand that tan^(-1)(x) means the angle whose tangent is x.
Step 2: Find tan^(-1)(1). The angle whose tangent is 1 is π/4 (or 45 degrees).
Step 3: Find tan^(-1)(√3). The angle whose tangent is √3 is π/3 (or 60 degrees).
Step 4: Add the two angles together: π/4 + π/3.
Step 5: To add π/4 and π/3, find a common denominator. The common denominator of 4 and 3 is 12.
Step 6: Convert π/4 to twelfths: π/4 = 3π/12.
Step 7: Convert π/3 to twelfths: π/3 = 4π/12.
Step 8: Now add the two fractions: 3π/12 + 4π/12 = 7π/12.
Step 9: Recognize that the sum of the angles is π/2 (or 90 degrees) because tan^(-1)(1) + tan^(-1)(√3) = π/2.

Inverse Trigonometric Functions – Understanding the values of inverse tangent functions and their properties.
Addition of Angles – Applying the addition of angles in trigonometric functions.