Square both sides. The answer we get for sin x + cos x may have the wrong sign, so we will have to chaeck that later.
sin^2 x + cos^2x + 2 sinx cosx = 2
1 + sin(2x) = 2
sin (2x) = 1
2x = pi/2 + 2 n pi where n is any integer
x = pi/4 + n pi
= pi/4, 5 pi/4
= 45 , 225 degrees
The first answer does not work because the sign is wrong, so the only answer between 0 and 360 degrees is 225 degees
Write an expression that gives all solutions to the equation
sin x + cos x = - radical 2
1 answer