Question

Find the general solution of the following equation: 

cos x – sin x = -1

Answer 1

To Find: General solution.

Given cos x - sin x = 1

⇒ cos(x + π/4) = - 1/√2 = cos 3π/4

[divide √2  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 θ = cos α

θ = 2kπ ± α, k ∈ l