# 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

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