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( or cos()
[Divide on both sides and cos(x-y) = cos x cos y - sin x sin y]
Formula used: cos = cos = 2n
By using above formula, we have
x - = 2n x = 2n +
x = 2n + or x = 2n - where n I
So general solution is x = 2n + or x = 2n - where n I