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If tan(x) = 1, what is the value of sin(x) + cos(x)?

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Question: If tan(x) = 1, what is the value of sin(x) + cos(x)?

Options:

  1. √2
  2. 1
  3. 0
  4. 2

Correct Answer: √2

Solution: 

If tan(x) = 1, then sin(x) = cos(x). Therefore, sin(x) + cos(x) = 2sin(x) = 2(1/√2) = √2.

If tan(x) = 1, what is the value of sin(x) + cos(x)?

Practice Questions

Q1
If tan(x) = 1, what is the value of sin(x) + cos(x)?
  1. √2
  2. 1
  3. 0
  4. 2

Questions & Step-by-Step Solutions

If tan(x) = 1, what is the value of sin(x) + cos(x)?
Correct Answer: √2
  • Step 1: Understand that tan(x) = sin(x) / cos(x).
  • Step 2: If tan(x) = 1, then sin(x) must equal cos(x) because sin(x) / cos(x) = 1 means they are the same.
  • Step 3: Let sin(x) = cos(x) = k for some value k.
  • Step 4: Since sin^2(x) + cos^2(x) = 1, we can write k^2 + k^2 = 1.
  • Step 5: This simplifies to 2k^2 = 1.
  • Step 6: Divide both sides by 2 to get k^2 = 1/2.
  • Step 7: Take the square root of both sides to find k = 1/√2.
  • Step 8: Now, since sin(x) = k and cos(x) = k, we have sin(x) + cos(x) = k + k = 2k.
  • Step 9: Substitute k = 1/√2 into 2k to get 2(1/√2).
  • Step 10: Simplify 2(1/√2) to get √2.
  • Trigonometric Identities – Understanding the relationship between sine, cosine, and tangent functions.
  • Pythagorean Identity – Using the identity sin²(x) + cos²(x) = 1 to derive values.
  • Angle Values – Recognizing specific angle values where trigonometric functions yield known results.
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