What is the general solution for (tan(x)+sqrt(3))(2sin(x)-1)=0 ?

The general solution for (tan(x)+sqrt(3))(2sin(x)-1)=0 is x=(2pi)/3+pin,x= pi/6+2pin,x=(5pi)/6+2pin

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Popular >

(tan(x)+sqrt(3))(2sin(x)-1)=0

Solution

(tan (x) + 3) (2 sin (x) - 1) = 0

Solution

x = \frac{2 π}{3} + πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 12 0^{\circ} + 18 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

(tan (x) + 3) (2 sin (x) - 1) = 0

Solving each part separately

tan (x) + 3 = 0 or 2 sin (x) - 1 = 0

tan (x) + 3 = 0 : x = \frac{2 π}{3} + πn

tan (x) + 3 = 0

Move

3

to the right side

tan (x) + 3 = 0

Subtract

3

from both sides

tan (x) + 3 - 3 = 0 - 3

Simplify

tan (x) = - 3

tan (x) = - 3

General solutions for

tan (x) = - 3

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

2 sin (x) - 1 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 sin (x) - 1 = 0

Move

1

to the right side

2 sin (x) - 1 = 0

Add

1

to both sides

2 sin (x) - 1 + 1 = 0 + 1

Simplify

2 sin (x) = 1

2 sin (x) = 1

Divide both sides by

2

2 sin (x) = 1

Divide both sides by

2

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

Simplify

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

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

General solutions for

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

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Popular Examples

sqrt(2)cos(3θ)+1=0

2 cos (3 θ) + 1 = 0

cos(a)=-3/5

cos (a) = - \frac{3}{5}

tan(x)=3.5

tan (x) = 3.5

sec(θ)= 1/(sec(θ))

sec (θ) = \frac{1}{sec ( θ )}

-2tan(θ)+1=3tan(θ)-7

- 2 tan (θ) + 1 = 3 tan (θ) - 7

Frequently Asked Questions (FAQ)

What is the general solution for (tan(x)+sqrt(3))(2sin(x)-1)=0 ?
The general solution for (tan(x)+sqrt(3))(2sin(x)-1)=0 is x=(2pi)/3+pin,x= pi/6+2pin,x=(5pi)/6+2pin