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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Popular Examples

cos(θ)=-5/8

cos (θ) = - \frac{5}{8}

(368.02)/(sin(66-x))=(290)/(sin(38))

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

cos^2(x)sec(x)=1

cos^{2} (x) sec (x) = 1

tan(x)=(9.3)/(7.5)

tan (x) = \frac{9.3}{7.5}

sin(α)+cos(α)=1

sin (α) + cos (α) = 1

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