What is the general solution for 2sqrt(3)cos(z)+2sin(z)=0 ?

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

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2sqrt(3)cos(z)+2sin(z)=0

23 cos (z) + 2 sin (z) = 0

z = \frac{2 π}{3} + πn

Solution steps

23 cos (z) + 2 sin (z) = 0

Rewrite using trig identities

23 + 2 tan (z) = 0

Move

23

to the right side

2 tan (z) = - 23

Divide both sides by

2

tan (z) = - 3

General solutions for

tan (z) = - 3

z = \frac{2 π}{3} + πn

\frac{cos ( x ) + cos ( 3 x )}{cos ^{2} ( x ) - sin ^{2} ( x )} = 0

sin (x) = 2 cos^{2} (x) - 1

tan (t) = \frac{- 5}{12}

\frac{( 1 - ( cos ( x ) ) ^{2} )}{( 1 + sin ( x ) )} = sin (x)

x, arctan (x) = 0

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