Solve the equation sin x - cos x=0.

To solve sinx-cosx =
0.

Solution:

Since
sin^2x+cos^2=1 is an identity, cosx = (1-sin^2x)^(1/2). So replacing cosx in the given
equation we get:

sinx +(1-sin^2)^(1/2) = 0.
Or

(1-sin^2x)^(1/2)=-sinx. squaring both
sides,

1-sin^2x =
sin^2x.Or

1=2sin^2x. Or

sin^2x
= 1/2. Or

sinx= sqrt(1/2) or sinx = -sqrt(1/2)
.

So x = pi/4 or 3pi/4 Or x= -pi/4 or 5pi/4 Or n*pi/4,
where n is an integer.

Or x= 45 degree, 135deg,225 deg or
315deg . or  n*45deg where n is an integer.