Verify the Identity sin(x)=cos(x)

Problem

sin(x)=cos(x)

Solution

1. Analyze the given equation to determine if it is an identity. An identity must be true for all values of x in the domain.

2. Test a specific value for x such as x=0

3. Evaluate the left side of the equation at x=0

sin(0)=0

4. Evaluate the right side of the equation at x=0

cos(0)=1

5. Compare the results. Since 0≠1 the equation does not hold for all values of x

6. Conclude that the equation is a conditional equation, not an identity. It is only true when tan(x)=1 such as x=π/4+n*π

Final Answer

sin(x)≠cos(x)* for all *x

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