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

The general solution for (tan(x)-1)(2cos(x)+1)=0 is x= pi/4+pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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(tan(x)-1)(2cos(x)+1)=0

Solution

(tan (x) - 1) (2 cos (x) + 1) = 0

Solution

x = \frac{π}{4} + πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

(tan (x) - 1) (2 cos (x) + 1) = 0

Solving each part separately

tan (x) - 1 = 0 or 2 cos (x) + 1 = 0

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

tan (x) - 1 = 0

Move

1

to the right side

tan (x) - 1 = 0

Add

1

to both sides

tan (x) - 1 + 1 = 0 + 1

Simplify

tan (x) = 1

tan (x) = 1

General solutions for

tan (x) = 1

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{π}{4} + πn

x = \frac{π}{4} + πn

2 cos (x) + 1 = 0 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

2 cos (x) + 1 = 0

Move

1

to the right side

2 cos (x) + 1 = 0

Subtract

1

from both sides

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

Simplify

2 cos (x) = - 1

2 cos (x) = - 1

Divide both sides by

2

2 cos (x) = - 1

Divide both sides by

2

\frac{2 cos ( x )}{2} = \frac{- 1}{2}

Simplify

cos (x) = - \frac{1}{2}

cos (x) = - \frac{1}{2}

General solutions for

cos (x) = - \frac{1}{2}

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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cot (θ) = - 3, sin (θ) < 0

tan(x)sin(x)+cos(x)=1

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6sin(t)=0

6 sin (t) = 0

(500*9.8*l(1-cos(θ)))=0.018

(500 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

sec(x)=(sin(x))/(cos(x))

sec (x) = \frac{sin ( x )}{cos ( x )}

Frequently Asked Questions (FAQ)

What is the general solution for (tan(x)-1)(2cos(x)+1)=0 ?
The general solution for (tan(x)-1)(2cos(x)+1)=0 is x= pi/4+pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin