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Evaluate the expression: tan^(-1)(1) + tan^(-1)(1) = ?

Practice Questions

Q1
Evaluate the expression: tan^(-1)(1) + tan^(-1)(1) = ?
  1. π/2
  2. π/4
  3. π/3
  4. π/6

Questions & Step-by-Step Solutions

Evaluate the expression: tan^(-1)(1) + tan^(-1)(1) = ?
Correct Answer: π/2
  • Step 1: Understand the expression tan^(-1)(1). This means we are looking for the angle whose tangent is 1.
  • Step 2: Recall that the tangent of π/4 (or 45 degrees) is 1. Therefore, tan^(-1)(1) = π/4.
  • Step 3: Now, we have tan^(-1)(1) + tan^(-1)(1). Since both are equal to π/4, we can write it as π/4 + π/4.
  • Step 4: Add the two angles together: π/4 + π/4 = 2 * (π/4) = π/2.
  • Step 5: The final answer is π/2.
  • Inverse Tangent Function – Understanding the properties and values of the inverse tangent function, particularly that tan^(-1)(1) equals π/4.
  • Addition of Angles – Applying the addition of angles in trigonometric functions, specifically how to sum two inverse tangent values.
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