Find all solutions to the equation. (sin x)(cos x) = 0

Solution:

Given equation (sin x)(cos x) = 0

⇒ sin x = 0

General solution is x = nπ ±(-1)ⁿ (0) when n ∈ Z.

⇒ cos x = 0

cos x = cos π/2

General solution is x = 2nπ ± π/2 when n ∈ Z.

Therefore the general solutions to the equation (sin x)(cos x) = 0 is x = nπ ±(-1)ⁿ (0) and x = 2nπ ± π/2 respectively when n ∈ Z.

Find all solutions to the equation. (sin x)(cos x) = 0

Summary:

The solutions to the equation (sin x)(cos x) = 0 is x = nπ ±(-1)ⁿ (0) and x = 2nπ ± π/2 respectively when n ∈ Z.