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Evaluate tan(sin^(-1)(1/√2)).

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Question: Evaluate tan(sin^(-1)(1/√2)).

Options:

  1. 1
  2. √2
  3. 0
  4. 2

Correct Answer: 1

Solution: 

If sin(x) = 1/√2, then x = π/4, thus tan(sin^(-1)(1/√2)) = tan(π/4) = 1.

Evaluate tan(sin^(-1)(1/√2)).

Practice Questions

Q1
Evaluate tan(sin^(-1)(1/√2)).
  1. 1
  2. √2
  3. 0
  4. 2

Questions & Step-by-Step Solutions

Evaluate tan(sin^(-1)(1/√2)).
  • Step 1: Understand that sin^(-1)(1/√2) means we are looking for an angle x such that sin(x) = 1/√2.
  • Step 2: Recall that sin(π/4) = 1/√2. Therefore, we can say that x = π/4.
  • Step 3: Now we need to find tan(x). Since we found that x = π/4, we need to calculate tan(π/4).
  • Step 4: Recall that tan(π/4) = 1.
  • Step 5: Therefore, tan(sin^(-1)(1/√2)) = tan(π/4) = 1.
  • Inverse Trigonometric Functions – Understanding how to evaluate inverse sine functions and their corresponding angles.
  • Trigonometric Identities – Applying the relationship between sine and tangent functions to find the value of tangent based on sine.
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