Solve for x cos(x)sin(x)-2cos(x)=0

Problem

cos(x)*sin(x)−2*cos(x)=0

Solution

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

cos(x)*(sin(x)−2)=0

2. Apply the zero product property by setting each individual factor equal to zero.

cos(x)=0

sin(x)−2=0

3. Solve the first equation for x by identifying the values where the cosine function is zero.

x=π/2+n*π

4. Solve the second equation by isolating the sine term.

sin(x)=2

5. Evaluate the range of the sine function, which is [−1,1] Since 2 is outside this range, the second equation has no real solutions.

sin(x)=2⇒No real solution

Final Answer

cos(x)*sin(x)−2*cos(x)=0⇒x=π/2+n*π

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