How to solve this equation? The topic is Radian Measure of Angle size.

Solve the equation for 0 ≤ x ≤ 2π.enter image source here

2 Answers
Jul 25, 2018

x=π3,4π3,3π4,7π4

Explanation:

tan2x+tanx=3tanx+3

tan2x+tanx3tanx3=0

tanx(tanx+1)3(tanx+1)=0

(tanx3)(tanx+1)=0

tanx3=0 or tanx+1=0

tanx3=0
tanx=3
x=π3,π+π3 --> tanx is positive in the first and third quadrant
x=π3,4π3


tanx+1=0
tanx=1
x=ππ4,2ππ4 --> tanx is negative in the second and fourth quadrant
x=3π4,7π4

Jul 25, 2018

π3,3π4,4π3,7π4

Explanation:

Given: tan2x+tanx=3tanx+3, in [0,2π]

Rearrange the equation to be =0:

tan2x+tanx3tanx3=0

Group factor:

(tan2x+tanx)+(3tanx3)=0

tanx(tanx+1)3(tanx+1)=0

(tanx+1)(tanx3)=0

tanx=1; tanx=3

The tangent is positive in quadrants I, III and negative in quadrants II & IV.

x=3π4,7π4; x=π3,4π3