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

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

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Popular Trigonometry >

2sec(x)tan(x)+2sec(x)+tan(x)+1=0

Solution

2 sec (x) tan (x) + 2 sec (x) + tan (x) + 1 = 0

Solution

x = \frac{3 π}{4} + πn

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

2 sec (x) tan (x) + 2 sec (x) + tan (x) + 1 = 0

Factor

2 sec (x) tan (x) + 2 sec (x) + tan (x) + 1 : (tan (x) + 1) (2 sec (x) + 1)

2 sec (x) tan (x) + 2 sec (x) + tan (x) + 1

= (2 sec (x) tan (x) + 2 sec (x)) + (tan (x) + 1)

Factor out

2 sec (x)

from

2 sec (x) tan (x) + 2 sec (x) : 2 sec (x) (tan (x) + 1)

2 sec (x) tan (x) + 2 sec (x)

Factor out common term

2 sec (x)

= 2 sec (x) (tan (x) + 1)

= (tan (x) + 1) + 2 sec (x) (tan (x) + 1)

Factor out common term

tan (x) + 1

= (tan (x) + 1) (2 sec (x) + 1)

(tan (x) + 1) (2 sec (x) + 1) = 0

Solving each part separately

tan (x) + 1 = 0 or 2 sec (x) + 1 = 0

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

tan (x) + 1 = 0

Move

1

to the right side

tan (x) + 1 = 0

Subtract

1

from 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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

2 sec (x) + 1 = 0 :

No Solution

2 sec (x) + 1 = 0

Move

1

to the right side

2 sec (x) + 1 = 0

Subtract

1

from both sides

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

Simplify

2 sec (x) = - 1

2 sec (x) = - 1

Divide both sides by

2

2 sec (x) = - 1

Divide both sides by

2

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

Simplify

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

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

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

Combine all the solutions

x = \frac{3 π}{4} + πn

Graph

Popular Examples

6tan^2(θ)cos(θ)+3tan^2(θ)=0

6 tan^{2} (θ) cos (θ) + 3 tan^{2} (θ) = 0

1=-cot(x)

1 = - cot (x)

1=sec(x)

1 = sec (x)

-0.5cos(x)+0.8660200000000…sin(x)=-0.5

- 0.5 cos (x) + 0.8660200000000 \dots sin (x) = - 0.5

csc^2(θ)=4

csc^{2} (θ) = 4

Frequently Asked Questions (FAQ)

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