solve this equation please... sin^2 (x) - cos^2 (x) = 0?

Question

from the interval [ 0, 2pi]

Answer 1

sin^2 (x) - cos^2 (x) = 0 <=>
-cos(2x) = 0 <=>
cos(2x) = 0 <=>
2x = pi/2 + n pi <=>
x = pi/4 + n pi/2, n is integer

To the interval [0, 2pi] belong: x= pi/4, 3pi/4, 5pi/4, 7pi/4

Answer 2

Since sin and cos are equal at both pi/4 and 5pi/4 sin^2-cos^2 will naturally equal 0. And since we are dealing with squared functions, the equation equals 0 when the sin and cos are opposite, or at 3pi/4 and 7pi/4.

Answer 3

That implies that sin^2(x) = cos^2(x)
which occurs only at pi/4, 3*pi/4, 5*pi/4 and 7*pi/4 (45 degrees, 135 degrees, etc)