Find the general solution of each of the following equations:
cos x – sin x = -1
To Find: General solution.
Given: cos x - sin x = 1 cos(x + ) = = cos
[divide on both sides and cos(x-y) = cos x cos y - sin x sin y]
So sin x = 0 or cos x = 0
Formula used: cos = cos = 2k , k I
x + = 2k x = 2k - x = 2k - or x = 2k -
x = 2k - or x = 2k
So general solution is x = 2n + or x = (2n-1) where n I