Solve for x sin(2theta)=cos(2theta)

Problem

sin(2*θ)=cos(2*θ)

Solution

1. Divide both sides of the equation by cos(2*θ) assuming cos(2*θ)≠0 to express the equation in terms of the tangent function.

sin(2*θ)/cos(2*θ)=1

2. Apply the trigonometric identity tan(x)=sin(x)/cos(x) to simplify the left side.

tan(2*θ)=1

3. Determine the general solution for the angle 2*θ by finding the inverse tangent of 1

2*θ=π/4+n*π

4. Isolate θ by dividing the entire expression by 2 where n is any integer.

θ=π/8+(n*π)/2

Final Answer

θ=π/8+(n*π)/2

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