If sinx+cosx= 1/(2^(1/2)) , then which of the following is true
(A) x can be in Quadrant I
(B) x must be in Quadrant II or IV
(C) x must be in Quadrant I or IV
(D) x can be in Quadrant I, II, or III
(E) none of the above is correct
sinx+cosx = 1/√2
√2 sin(x + π/4) = 1/√2
sin(x + π/4) = -1/2
so x + π/4 is in QIII or QIV
a little checking should convince you that x is in QII or QIV