Solve for x cos(x)-tan(x)cos(x)=0

Problem

cos(x)−tan(x)*cos(x)=0

Solution

1. Factor out the common term cos(x) from the left side of the equation.

cos(x)*(1−tan(x))=0

2. Apply the zero product property to set each factor equal to zero.

cos(x)=0

1−tan(x)=0

3. Solve for x in the first equation cos(x)=0 by identifying where the cosine function is zero on the unit circle.

x=π/2+n*π

4. Isolate the tangent function in the second equation 1−tan(x)=0

tan(x)=1

5. Solve for x in the equation tan(x)=1 by identifying where the tangent function equals one.

x=π/4+n*π

6. Check for domain restrictions because tan(x) is undefined when cos(x)=0 Since the original equation contains tan(x) the solutions from cos(x)=0 (where x=π/2+n*π must be excluded.

x≠π/2+n*π

Final Answer

cos(x)−tan(x)*cos(x)=0⇒x=π/4+n*π

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