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Evaluate tan^(-1)(1) + tan^(-1)(1).

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

Options:

  1. π/2
  2. π/4
  3. π/3
  4. 0

Correct Answer: π/2

Solution: 

tan^(-1)(1) = π/4, thus tan^(-1)(1) + tan^(-1)(1) = π/4 + π/4 = π/2.

Evaluate tan^(-1)(1) + tan^(-1)(1).

Practice Questions

Q1
Evaluate tan^(-1)(1) + tan^(-1)(1).
  1. π/2
  2. π/4
  3. π/3
  4. 0

Questions & Step-by-Step Solutions

Evaluate tan^(-1)(1) + tan^(-1)(1).
Correct Answer: π/2
  • Step 1: Understand that tan^(-1)(1) means the angle whose tangent is 1.
  • Step 2: Recall that the angle whose tangent is 1 is π/4 (or 45 degrees).
  • Step 3: Since we have tan^(-1)(1) + tan^(-1)(1), we can replace each tan^(-1)(1) with π/4.
  • Step 4: Now, add π/4 + π/4.
  • Step 5: π/4 + π/4 equals 2 * (π/4), which simplifies to π/2.
  • Inverse Trigonometric Functions – Understanding the values of inverse trigonometric functions, specifically tan^(-1)(x) and its properties.
  • Addition of Angles – Applying the addition of angles in trigonometric functions, particularly when dealing with the sum of inverse tangent values.
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