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If x = tan^(-1)(√3), then what is the value of sin^(-1)(x)?

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Question: If x = tan^(-1)(√3), then what is the value of sin^(-1)(x)?

Options:

  1. π/3
  2. π/4
  3. π/2
  4. π/6

Correct Answer: π/3

Solution: 

x = tan^(-1)(√3) = π/3, thus sin^(-1)(x) = sin^(-1)(√3/2) = π/3.

If x = tan^(-1)(√3), then what is the value of sin^(-1)(x)?

Practice Questions

Q1
If x = tan^(-1)(√3), then what is the value of sin^(-1)(x)?
  1. π/3
  2. π/4
  3. π/2
  4. π/6

Questions & Step-by-Step Solutions

If x = tan^(-1)(√3), then what is the value of sin^(-1)(x)?
  • Step 1: Understand that x = tan^(-1)(√3) means we need to find an angle whose tangent is √3.
  • Step 2: Recall that tan(π/3) = √3. Therefore, x = π/3.
  • Step 3: Now we need to find sin^(-1)(x), which is sin^(-1)(π/3).
  • Step 4: We know that sin(π/3) = √3/2.
  • Step 5: Therefore, sin^(-1)(√3/2) = π/3.
  • Inverse Trigonometric Functions – Understanding the relationships between inverse trigonometric functions such as tan^(-1) and sin^(-1).
  • Trigonometric Values – Knowledge of standard angles and their sine, cosine, and tangent values.
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