text: a  trigonometry question? if sinx+cosx=sqrt2 sin2x=? cosx=? x=? (sinx+cosx)squared = 2 (sinx)squared + 2sinxcosx + (cosx)squared = 2  [since (a+b)squared = (a)squared +2ab + (b)squared ]  now u know that (sinx)squared  + (cosx)squared = 1 therefore the above equation becomes  1 + 2sinxcosx = 2 i.e. 2sinxcosx = 1 i.e. sin2x =1 (since sin2x = 2sinxcosx ) now we know that sin (90) degree = 1 therefore here 2x = 90 degree i.e x = 45 degree i.e cos x = cos 45 = 1/sqrt(2)