Secondary maths!!!!! 100quick!

Symbol § = square root

You must know the transformation of a sinX + b sinX
a sin X + b cos X = § (a^2 + b^2) cos (X – Y), where tan Y = a/b

(1/§2) cos x - (1/§2) sin x
a = (1/§2), b = (-1/§2)
§ (a^2 + b^2) = § [(1/§2)^2 + (-1/§2)^2] = § [1/2 + ½] = §(1) = 1

(1/§2) cos x - (1/§2) sin x = 1 cos (X-Y), where tan Y =(1/§2)/(-1/§2) =-1
tan Y = -1, Y = 135˚ or 315˚
1 sin X - 1 cos X = 1 cos (X – 135˚)
1 sin X - 1 cos X = cos (X – 135˚) or cos (X – 315˚)

Check:
Let X = 180˚

(1/§2) cos 180˚ - (1/§2) sin 180˚ = cos (180˚ - 135˚)
(1/§2) (1) - (1/§2) (0) = cos (45˚)
(1/§2) = cos (45˚)

Let X = 360˚
(1/§2) cos 180˚ - (1/§2) sin 180˚ = cos (180˚ - 135˚)
(1/§2) (1) - (1/§2) (0) = cos (360˚ - 135˚)
(1/§2) = cos (45˚)


(1/§2 )sin X - (1/§2) cos X = cos (X – 135˚) …. or
(1/§2) sin X - (1/§2) cos X = cos (X – 315˚)