Which is the value of x for sinx=cosx?

For the beginning, we could give a simple answer:
x=pi/4.

Let's solve the
equation:

sin x - cos
x=0

We'll divide the equation by (cos x) and we'll
get:

sin x /cos x - 1 =0

The
ratio sinx/cosx = tanx

tan x -1
=0

We'll add 1 both sides:

tan
x = 1

x= arctan 1 + k*pi

x =
pi/4 + k*pi

pi/4=45
degrees.

We could also make the remark that if the ratio
sin x / cos x=1, the terms from numerator and denominator are equal => sin x =
cosx.

If sin x = cos x => the angles  of
the  triangle are equal, too, so, in a right angle triangle, the angles could only be =
45 degrees (the conclusion is based on fact that in a triangle, the sum of angles is 180
degrees, and one of them is 90 degrees and the other 2 are equals, so 90 +
2*x=180.

2*x=180-90

x=90/2

x=45
degrees