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If tan(x) = 1, what is the value of sin(x) + cos(x)?
If tan(x) = 1, what is the value of sin(x) + cos(x)?
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Practice Questions
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Q1
If tan(x) = 1, what is the value of sin(x) + cos(x)?
√2
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If tan(x) = 1, then sin(x) = cos(x). Therefore, sin(x) + cos(x) = 2sin(x) = 2(1/√2) = √2.
Questions & Step-by-step Solutions
1 item
Q
Q: If tan(x) = 1, what is the value of sin(x) + cos(x)?
Solution:
If tan(x) = 1, then sin(x) = cos(x). Therefore, sin(x) + cos(x) = 2sin(x) = 2(1/√2) = √2.
Steps: 10
Show Steps
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.
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