What are the solutions of the equation cos(x) + sin(x) = 1?
Practice Questions
1 question
Q1
What are the solutions of the equation cos(x) + sin(x) = 1?
x = 0
x = π/4
x = π/2
x = π
The only solution is x = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: What are the solutions of the equation cos(x) + sin(x) = 1?
Solution: The only solution is x = 0.
Steps: 7
Step 1: Start with the equation cos(x) + sin(x) = 1.
Step 2: Recall that the maximum value of cos(x) is 1 and the maximum value of sin(x) is also 1.
Step 3: Since both cos(x) and sin(x) are at most 1, the only way their sum can equal 1 is if one of them is 1 and the other is 0.
Step 4: Check when cos(x) = 1. This happens at x = 0.
Step 5: If cos(0) = 1, then sin(0) = 0. So, cos(0) + sin(0) = 1 + 0 = 1.
Step 6: Check if there are any other angles where cos(x) + sin(x) = 1. For any other angle, either cos(x) or sin(x) will be less than 1, making their sum less than 1.
Step 7: Conclude that the only solution to the equation is x = 0.
