Solve for x cot(x)cos(x)^2=2cot(x)

Problem

cot(x)*cos(x)=2*cot(x)

Solution

1. Rearrange the equation by subtracting 2*cot(x) from both sides to set the equation to zero.

cot(x)*cos(x)−2*cot(x)=0

2. Factor out the common term cot(x) from the expression.

cot(x)*(cos(x)−2)=0

3. Set each factor to zero using the zero product property.

cot(x)=0

cos(x)−2=0

4. Solve the first case where cot(x)=0 This occurs when cos(x)=0

x=π/2+n*π

5. Solve the second case where cos(x)−2=0

cos(x)=2

cos(x)=±√(,2)

6. Evaluate the validity of the second case. Since the range of cos(x) is [−1,1] and √(,2)≈1.414 there are no real solutions for this part.

cos(x)=±√(,2)⇒No solution

Final Answer

cot(x)*cos(x)=2*cot(x)⇒x=π/2+n*π

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