Question 808520
Given:
(1) {{{-sin2x = sqrt(2)*cosx}}}
Use the trig identity for double-angle formulas
(2) {{{sin2x = 2sinx*cosx}}} and get
(3) {{{-2sinx*cosx = sqrt(2)*cosx}}}
Now as long as cos(x) is not equal to zero (to be verified) we can divide both sides of (3) by cos(x) and get
(4) {{{sinx = -1/sqrt(2)}}} or
(5) {{{x = arcsin(-1/sqrt(2))}}}  or
(6) x = 225 and 315 degrees. 
Since neither angle has it's cosine equal to zero, the division by cosx in (3) was allowed.
Answer: x = {225,315} degrees.