What is the general solution for 0=sqrt(3)cos(x)+sin(x) ?

The general solution for 0=sqrt(3)cos(x)+sin(x) is x=(2pi)/3+pin

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

0 = 3 cos (x) + sin (x)

x = \frac{2 π}{3} + πn

Solution steps

0 = 3 cos (x) + sin (x)

Switch sides

3 cos (x) + sin (x) = 0

Rewrite using trig identities

3 + tan (x) = 0

Move

3

to the right side

tan (x) = - 3

General solutions for

tan (x) = - 3

x = \frac{2 π}{3} + πn

- 4 cos (2 θ) - 1 = - 2 cos (θ)

cos^{3} (x) = 1

7 cos^{3} (x) = 7 cos (x)

0 = - 2 sin (x)

cos (2 θ) - 3 cos (θ) = 0

What is the general solution for 0=sqrt(3)cos(x)+sin(x) ?
The general solution for 0=sqrt(3)cos(x)+sin(x) is x=(2pi)/3+pin