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What is the value of sin^(-1)(1/2) + sin^(-1)(√3/2)?

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Question: What is the value of sin^(-1)(1/2) + sin^(-1)(√3/2)?

Options:

  1. π/3
  2. π/2
  3. 2π/3
  4. π

Correct Answer: π/2

Solution: 

sin^(-1)(1/2) = π/6 and sin^(-1)(√3/2) = π/3. Therefore, π/6 + π/3 = π/2.

What is the value of sin^(-1)(1/2) + sin^(-1)(√3/2)?

Practice Questions

Q1
What is the value of sin^(-1)(1/2) + sin^(-1)(√3/2)?
  1. π/3
  2. π/2
  3. 2π/3
  4. π

Questions & Step-by-Step Solutions

What is the value of sin^(-1)(1/2) + sin^(-1)(√3/2)?
Correct Answer: π/2
  • Step 1: Understand that sin^(-1)(x) means the angle whose sine is x.
  • Step 2: Find sin^(-1)(1/2). The angle whose sine is 1/2 is π/6 (30 degrees).
  • Step 3: Find sin^(-1)(√3/2). The angle whose sine is √3/2 is π/3 (60 degrees).
  • Step 4: Add the two angles together: π/6 + π/3.
  • Step 5: To add π/6 and π/3, convert π/3 to a fraction with a common denominator: π/3 = 2π/6.
  • Step 6: Now add π/6 + 2π/6 = 3π/6.
  • Step 7: Simplify 3π/6 to π/2.
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