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Find the general solution of the equation sin(x) = sin(2x).
Find the general solution of the equation sin(x) = sin(2x).
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Practice Questions
1 question
Q1
Find the general solution of the equation sin(x) = sin(2x).
x = nπ
x = nπ/3
x = nπ/2
x = nπ/4
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Using the identity sin(a) = sin(b) gives x = nπ or x = (2n+1)π/3.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the general solution of the equation sin(x) = sin(2x).
Solution:
Using the identity sin(a) = sin(b) gives x = nπ or x = (2n+1)π/3.
Steps: 8
Show Steps
Step 1: Start with the equation sin(x) = sin(2x).
Step 2: Use the identity sin(a) = sin(b), which means a = b + 2nπ or a = π - b + 2nπ for any integer n.
Step 3: Set up the first case: x = 2x + 2nπ.
Step 4: Rearrange the first case to find x: x - 2x = 2nπ, which simplifies to -x = 2nπ, so x = -2nπ.
Step 5: Set up the second case: x = π - 2x + 2nπ.
Step 6: Rearrange the second case to find x: x + 2x = π + 2nπ, which simplifies to 3x = π + 2nπ, so x = (π + 2nπ) / 3.
Step 7: Combine the solutions from both cases: x = -2nπ and x = (π + 2nπ) / 3.
Step 8: Notice that (π + 2nπ) / 3 can be rewritten as (2n + 1)π / 3 for clarity.
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