What is the general solution for 5sin(x)tan(x)-10tan(x)+3sin(x)-6=0 ?

The general solution for 5sin(x)tan(x)-10tan(x)+3sin(x)-6=0 is x=-0.54041…+pin

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Popular >

5sin(x)tan(x)-10tan(x)+3sin(x)-6=0

Solution

5 sin (x) tan (x) - 10 tan (x) + 3 sin (x) - 6 = 0

Solution

x = - 0.54041 \dots + πn

Degrees

x = - 30.96375 \dots^{\circ} + 18 0^{\circ} n

Solution steps

5 sin (x) tan (x) - 10 tan (x) + 3 sin (x) - 6 = 0

Factor

5 sin (x) tan (x) - 10 tan (x) + 3 sin (x) - 6 : (sin (x) - 2) (5 tan (x) + 3)

5 sin (x) tan (x) - 10 tan (x) + 3 sin (x) - 6

= (5 sin (x) tan (x) - 10 tan (x)) + (3 sin (x) - 6)

Factor out

3

from

3 sin (x) - 6 : 3 (sin (x) - 2)

3 sin (x) - 6

Rewrite

- 6

2 \cdot 3

= 3 sin (x) + 2 \cdot 3

Factor out common term

3

= 3 (sin (x) - 2)

Factor out

5 tan (x)

from

5 sin (x) tan (x) - 10 tan (x) : 5 tan (x) (sin (x) - 2)

5 sin (x) tan (x) - 10 tan (x)

Rewrite

- 10

2 \cdot 5

= 5 sin (x) tan (x) + 2 \cdot 5 tan (x)

Factor out common term

5 tan (x)

= 5 tan (x) (sin (x) - 2)

= 3 (sin (x) - 2) + 5 tan (x) (sin (x) - 2)

Factor out common term

sin (x) - 2

= (sin (x) - 2) (5 tan (x) + 3)

(sin (x) - 2) (5 tan (x) + 3) = 0

Solving each part separately

sin (x) - 2 = 0 or 5 tan (x) + 3 = 0

sin (x) - 2 = 0 :

No Solution

sin (x) - 2 = 0

Move

2

to the right side

sin (x) - 2 = 0

Add

2

to both sides

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

Simplify

sin (x) = 2

sin (x) = 2

- 1 \leq sin (x) \leq 1

No Solution

5 tan (x) + 3 = 0 : x = arctan (- \frac{3}{5}) + πn

5 tan (x) + 3 = 0

Move

3

to the right side

5 tan (x) + 3 = 0

Subtract

3

from both sides

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

Simplify

5 tan (x) = - 3

5 tan (x) = - 3

Divide both sides by

5

5 tan (x) = - 3

Divide both sides by

5

\frac{5 tan ( x )}{5} = \frac{- 3}{5}

Simplify

tan (x) = - \frac{3}{5}

tan (x) = - \frac{3}{5}

Apply trig inverse properties

tan (x) = - \frac{3}{5}

General solutions for

tan (x) = - \frac{3}{5}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{3}{5}) + πn

x = arctan (- \frac{3}{5}) + πn

Combine all the solutions

x = arctan (- \frac{3}{5}) + πn

Show solutions in decimal form

x = - 0.54041 \dots + πn

Popular Examples

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tan (2 x) = \frac{3}{4}

sin(x)=1+cos(x)

sin (x) = 1 + cos (x)

Frequently Asked Questions (FAQ)

What is the general solution for 5sin(x)tan(x)-10tan(x)+3sin(x)-6=0 ?
The general solution for 5sin(x)tan(x)-10tan(x)+3sin(x)-6=0 is x=-0.54041…+pin