What is the general solution for 10tan(b)+12=tan(b)+6 ?

The general solution for 10tan(b)+12=tan(b)+6 is b=-0.58800…+pin

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Popular Trigonometry >

10tan(b)+12=tan(b)+6

Solution

10 tan (b) + 12 = tan (b) + 6

Solution

b = - 0.58800 \dots + πn

Degrees

b = - 33.69006 \dots^{\circ} + 18 0^{\circ} n

Solution steps

10 tan (b) + 12 = tan (b) + 6

Solve by substitution

10 tan (b) + 12 = tan (b) + 6

Let:

tan (b) = u

10 u + 12 = u + 6

10 u + 12 = u + 6 : u = - \frac{2}{3}

10 u + 12 = u + 6

Move

12

to the right side

10 u + 12 = u + 6

Subtract

12

from both sides

10 u + 12 - 12 = u + 6 - 12

Simplify

10 u = u - 6

10 u = u - 6

Move

u

to the left side

10 u = u - 6

Subtract

u

from both sides

10 u - u = u - 6 - u

Simplify

9 u = - 6

9 u = - 6

Divide both sides by

9

9 u = - 6

Divide both sides by

9

\frac{9 u}{9} = \frac{- 6}{9}

Simplify

\frac{9 u}{9} = \frac{- 6}{9}

Simplify

\frac{9 u}{9} : u

\frac{9 u}{9}

Divide the numbers:

\frac{9}{9} = 1

= u

Simplify

\frac{- 6}{9} : - \frac{2}{3}

\frac{- 6}{9}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{6}{9}

Cancel the common factor:

3

= - \frac{2}{3}

u = - \frac{2}{3}

u = - \frac{2}{3}

u = - \frac{2}{3}

Substitute back

u = tan (b)

tan (b) = - \frac{2}{3}

tan (b) = - \frac{2}{3}

tan (b) = - \frac{2}{3} : b = arctan (- \frac{2}{3}) + πn

tan (b) = - \frac{2}{3}

Apply trig inverse properties

tan (b) = - \frac{2}{3}

General solutions for

tan (b) = - \frac{2}{3}

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

b = arctan (- \frac{2}{3}) + πn

b = arctan (- \frac{2}{3}) + πn

Combine all the solutions

b = arctan (- \frac{2}{3}) + πn

Show solutions in decimal form

b = - 0.58800 \dots + πn

Graph

Popular Examples

arctan(x)+arctan(1-x)=arctan(4/3)

arctan (x) + arctan (1 - x) = arctan (\frac{4}{3})

cos(θ)=(-8)/(sqrt(14)*\sqrt{20)}

cos (θ) = \frac{- 8}{14 \cdot 20}

sin^2(x)= 1/3

sin^{2} (x) = \frac{1}{3}

cos(2x)=-0.8

cos (2 x) = - 0.8

0=-4sin(2x)

0 = - 4 sin (2 x)

Frequently Asked Questions (FAQ)

What is the general solution for 10tan(b)+12=tan(b)+6 ?
The general solution for 10tan(b)+12=tan(b)+6 is b=-0.58800…+pin