What is the general solution for 5cos(x)tan(x)+3tan(x)=0 ?

The general solution for 5cos(x)tan(x)+3tan(x)=0 is x=pin,x=2.21429…+2pin,x=-2.21429…+2pin

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5cos(x)tan(x)+3tan(x)=0

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

x = πn, x = 2.21429 \dots + 2 πn, x = - 2.21429 \dots + 2 πn

Solution steps

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

Factor

5 cos (x) tan (x) + 3 tan (x) : tan (x) (5 cos (x) + 3)

tan (x) (5 cos (x) + 3) = 0

Solving each part separately

tan (x) = 0 or 5 cos (x) + 3 = 0

tan (x) = 0 : x = πn

5 cos (x) + 3 = 0 : x = arccos (- \frac{3}{5}) + 2 πn, x = - arccos (- \frac{3}{5}) + 2 πn

Combine all the solutions

x = πn, x = arccos (- \frac{3}{5}) + 2 πn, x = - arccos (- \frac{3}{5}) + 2 πn

Show solutions in decimal form

x = πn, x = 2.21429 \dots + 2 πn, x = - 2.21429 \dots + 2 πn

2 sec (θ) + 2 = 6

4 cos (x) tan (x) = 3 tan (x)

3 sin (x) = 1 + sin (x)

2 sin (x - \frac{π}{6}) + 1 = 0

3 - 3 sin (θ) = 6 cos^{2} (θ)

What is the general solution for 5cos(x)tan(x)+3tan(x)=0 ?
The general solution for 5cos(x)tan(x)+3tan(x)=0 is x=pin,x=2.21429…+2pin,x=-2.21429…+2pin