What is the general solution for sin(3x)=sqrt(3)cos(3x) ?

The general solution for sin(3x)=sqrt(3)cos(3x) is x= pi/9+(pin)/3

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sin(3x)=sqrt(3)cos(3x)

sin (3 x) = 3 cos (3 x)

x = \frac{π}{9} + \frac{πn}{3}

Solution steps

sin (3 x) = 3 cos (3 x)

Rewrite using trig identities

tan (3 x) = 3

General solutions for

tan (3 x) = 3

3 x = \frac{π}{3} + πn

Solve

3 x = \frac{π}{3} + πn : x = \frac{π}{9} + \frac{πn}{3}

x = \frac{π}{9} + \frac{πn}{3}

(9 sin (2 x) + 9 cos (2 x))^{2} = 81

- 2 cos^{2} (θ) + sin (θ) - 3 = - 4

sec^{2} (x) - 9 sec (x) = 0

- 3 sin (2 θ) = 5 cos (2 θ)

(tan^{2} (θ) - 4) (2 cos (θ) + 1) = 0

What is the general solution for sin(3x)=sqrt(3)cos(3x) ?
The general solution for sin(3x)=sqrt(3)cos(3x) is x= pi/9+(pin)/3