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If sin A = 1/√2, what is the value of tan A?

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Question: If sin A = 1/√2, what is the value of tan A?

Options:

  1. 1
  2. √2
  3. 2
  4. 1/2

Correct Answer: 1

Solution: 

tan A = sin A / cos A = (1/√2) / (1/√2) = 1.

If sin A = 1/√2, what is the value of tan A?

Practice Questions

Q1
If sin A = 1/√2, what is the value of tan A?
  1. 1
  2. √2
  3. 2
  4. 1/2

Questions & Step-by-Step Solutions

If sin A = 1/√2, what is the value of tan A?
  • Step 1: We know that sin A = 1/√2.
  • Step 2: We need to find cos A. Since sin^2 A + cos^2 A = 1, we can find cos A.
  • Step 3: Calculate sin^2 A: (1/√2)^2 = 1/2.
  • Step 4: Substitute sin^2 A into the equation: 1/2 + cos^2 A = 1.
  • Step 5: Solve for cos^2 A: cos^2 A = 1 - 1/2 = 1/2.
  • Step 6: Take the square root to find cos A: cos A = 1/√2.
  • Step 7: Now we can find tan A using the formula tan A = sin A / cos A.
  • Step 8: Substitute the values: tan A = (1/√2) / (1/√2).
  • Step 9: Simplify the fraction: tan A = 1.
  • Trigonometric Ratios – Understanding the relationship between sine, cosine, and tangent functions.
  • Pythagorean Identity – Using the identity sin²A + cos²A = 1 to find cos A when sin A is known.
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