Math help please. what is the answer to: cos2x - sin2x + 1 = 0

cos2x - sin2x + 1= 0 (Note the 2 is NOT an exponent) could someone please explain how to do this problem? any help is greatly appreciated.

1) cos(2x) + 1 = sin(2x)

sin can not be larger than 1, so since you add 1 in the equation,

cos(2x) can
1)
only be 0 , and sin(2x) = 1
in this case is x = pi/4

or
2)
cos(2x) = -1, and sin(2x) = 0
in this case is x = pi/2
-------

or for the solution x = pi/4 use the identities
sin(2x) = 2tan(x)/(1 + tan^2(x))
cos(2x) = (1 - tan^2(x)/(1 + tan^2(x))

(1 - tan^2(x)/(1 + tan^2(x)) - 2tan(x)/(1 + tan^2(x)) + 1 = 0
(1 - tan^2(x) - 2tan(x) + (1 + tan^2(x) = 0
2 - 2tan(x) = 0
tan(x) = 1
x = pi/4


OG