Solve for x (sin(x))(cos(x))=0

Problem

sin(x)*cos(x)=0

Solution

1. Apply the Zero Product Property to the equation, which states that if the product of two factors is zero, at least one of the factors must be zero.

sin(x)=0

cos(x)=0

2. Solve the first equation sin(x)=0 for x The sine function is zero at integer multiples of π

x=n*π

where *n* is any integer

3. Solve the second equation cos(x)=0 for x The cosine function is zero at odd multiples of π/2

x=π/2+n*π

where *n* is any integer

4. Combine the solutions into a single expression. The values 0,π/2,π,(3*π)/2,… can be represented as multiples of π/2

x=(n*π)/2

Final Answer

sin(x)*cos(x)=0⇒x=(n*π)/2

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