What is the general solution for 3tan(x)+2cos(x)=0 ?

The general solution for 3tan(x)+2cos(x)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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3tan(x)+2cos(x)=0

3 tan (x) + 2 cos (x) = 0

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

3 tan (x) + 2 cos (x) = 0

Express with sin, cos

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

(1 - sin^{2} (x)) \cdot 2 + 3 sin (x) = 0

Solve by substitution

sin (x) = - \frac{1}{2}, sin (x) = 2

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = 2 :

No Solution

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

(cos (x)) (b sin (x) - a) = 0, 0 \leq x < 2 π

cos (x) = - \frac{5}{34}

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

sec (θ) = - \frac{1}{2}

cos (x) = cos (x - c)

What is the general solution for 3tan(x)+2cos(x)=0 ?
The general solution for 3tan(x)+2cos(x)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin