Solve for x square root of 3sin(2x)=cos(2x)

Problem

√(,3)*sin(2*x)=cos(2*x)

Solution

1. Divide both sides of the equation by cos(2*x) to group the trigonometric functions, assuming cos(2*x)≠0

(√(,3)*sin(2*x))/cos(2*x)=1

2. Substitute the identity tan(θ)=sin(θ)/cos(θ) into the equation.

√(,3)*tan(2*x)=1

3. Isolate the tangent function by dividing both sides by √(,3)

tan(2*x)=1/√(,3)

4. Determine the general solution for the angle 2*x by finding the arctangent of 1/√(,3)

2*x=π/6+n*π

5. Solve for x by dividing the entire expression by 2 where n is any integer.

x=π/12+(n*π)/2

Final Answer

√(,3)*sin(2*x)=cos(2*x)⇒x=π/12+(n*π)/2

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