how do you solve sinx=cosx??

To solve the equation sin(x) = cos(x), we can use some trigonometric identities and properties. Here's a step-by-step solution:

1. Begin by rewriting the equation using the identity sin(x) = cos(90° - x), since sin(x) and cos(x) are equal when their arguments differ by 90 degrees.
cos(90° - x) = cos(x)

2. Now, we have a cosine equation. Use the identity cos(a) = cos(-a) to simplify the equation.
cos(90° - x) = cos(-x)

3. Apply the identity cos(a) = cos(b) if and only if a = ± b. Equate the arguments of cosine to find the possible values of x.
90° - x = ±x

4. Solve for x. Separate the equation into two cases by considering the positive and negative signs of ±x.

Case 1: 90° - x = x
90° = 2x
x = 90° / 2
x = 45°

Case 2: 90° - x = -x
90° = x - x
90° = 0° (This is not a valid solution)

5. Therefore, the only solution to the equation sin(x) = cos(x) is x = 45°.

So, the solution to sin(x) = cos(x) is x = 45°, which means the values of sine and cosine are equal at the angle 45 degrees.