What is the general solution for sin(2θ)=-sqrt(3)cos(2θ) ?

The general solution for sin(2θ)=-sqrt(3)cos(2θ) is θ= pi/3+(pin)/2

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sin(2θ)=-sqrt(3)cos(2θ)

sin (2 θ) = - 3 cos (2 θ)

θ = \frac{π}{3} + \frac{πn}{2}

Solution steps

sin (2 θ) = - 3 cos (2 θ)

Rewrite using trig identities

tan (2 θ) = - 3

General solutions for

tan (2 θ) = - 3

2 θ = \frac{2 π}{3} + πn

Solve

2 θ = \frac{2 π}{3} + πn : θ = \frac{π}{3} + \frac{πn}{2}

θ = \frac{π}{3} + \frac{πn}{2}

4 sec (θ) - 4 = 0

sin (2 x) + 6 cos (x) = 0

cos (3 x) = \frac{1}{2}, 0 \leq x \leq 2 π

2 cos^{2} (x) - cos (x) = 0, 0 \leq x < 2 π

- 2 cos^{2} (x) = cos (x)

What is the general solution for sin(2θ)=-sqrt(3)cos(2θ) ?
The general solution for sin(2θ)=-sqrt(3)cos(2θ) is θ= pi/3+(pin)/2