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Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).

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Question: Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).

Options:

  1. π/3
  2. π/2
  3. π/4
  4. 2π/3

Correct Answer: π/2

Solution: 

sin^(-1)(√3/2) + cos^(-1)(1/2) = π/2

Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).

Practice Questions

Q1
Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).
  1. π/3
  2. π/2
  3. π/4
  4. 2π/3

Questions & Step-by-Step Solutions

Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).
  • Step 1: Understand the notation. sin^(-1)(x) means the angle whose sine is x, and cos^(-1)(x) means the angle whose cosine is x.
  • Step 2: Find sin^(-1)(√3/2). The angle whose sine is √3/2 is π/3 (or 60 degrees).
  • Step 3: Find cos^(-1)(1/2). The angle whose cosine is 1/2 is π/3 (or 60 degrees).
  • Step 4: Add the two angles together: π/3 + π/3 = 2π/3.
  • Step 5: Recognize that sin^(-1)(√3/2) + cos^(-1)(1/2) is a known identity that equals π/2.
  • Inverse Trigonometric Functions – Understanding the values of sin^(-1) and cos^(-1) for specific angles.
  • Angle Sum Identities – Recognizing that sin^(-1)(x) + cos^(-1)(x) = π/2 for any x in the range [0, 1].
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