What is the general solution for 4cos(x)tan(x)-3tan(x)=0 ?

The general solution for 4cos(x)tan(x)-3tan(x)=0 is x=pin,x=0.72273…+2pin,x=2pi-0.72273…+2pin

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4cos(x)tan(x)-3tan(x)=0

4 cos (x) tan (x) - 3 tan (x) = 0

x = πn, x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Solution steps

4 cos (x) tan (x) - 3 tan (x) = 0

Factor

4 cos (x) tan (x) - 3 tan (x) : tan (x) (4 cos (x) - 3)

tan (x) (4 cos (x) - 3) = 0

Solving each part separately

tan (x) = 0 or 4 cos (x) - 3 = 0

tan (x) = 0 : x = πn

4 cos (x) - 3 = 0 : x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

Combine all the solutions

x = πn, x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

Show solutions in decimal form

x = πn, x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

cos (x) sin (x) = 2 sin (x)

sin (x) = 2 cos (x)

sec (x) tan (x) = 0

2 cos (x) + 1 = 3

sec (x) + tan (x) = 0

What is the general solution for 4cos(x)tan(x)-3tan(x)=0 ?
The general solution for 4cos(x)tan(x)-3tan(x)=0 is x=pin,x=0.72273…+2pin,x=2pi-0.72273…+2pin