What is the general solution for 100tan(x)-8=50tan(x) ?

The general solution for 100tan(x)-8=50tan(x) is x=0.15865…+pin

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100tan(x)-8=50tan(x)

100 tan (x) - 8 = 50 tan (x)

x = 0.15865 \dots + πn

Degrees

x = 9.09027 \dots^{\circ} + 18 0^{\circ} n

Solution steps

100 tan (x) - 8 = 50 tan (x)

Solve by substitution

100 tan (x) - 8 = 50 tan (x)

Let:

tan (x) = u

100 u - 8 = 50 u

100 u - 8 = 50 u : u = \frac{4}{25}

100 u - 8 = 50 u

Move

8

to the right side

100 u - 8 = 50 u

Add

8

to both sides

100 u - 8 + 8 = 50 u + 8

Simplify

100 u = 50 u + 8

100 u = 50 u + 8

Move

50 u

to the left side

100 u = 50 u + 8

Subtract

50 u

from both sides

100 u - 50 u = 50 u + 8 - 50 u

Simplify

50 u = 8

50 u = 8

Divide both sides by

50

50 u = 8

Divide both sides by

50

\frac{50 u}{50} = \frac{8}{50}

Simplify

u = \frac{4}{25}

u = \frac{4}{25}

Substitute back

u = tan (x)

tan (x) = \frac{4}{25}

tan (x) = \frac{4}{25}

tan (x) = \frac{4}{25} : x = arctan (\frac{4}{25}) + πn

tan (x) = \frac{4}{25}

Apply trig inverse properties

tan (x) = \frac{4}{25}

General solutions for

tan (x) = \frac{4}{25}

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

x = arctan (\frac{4}{25}) + πn

x = arctan (\frac{4}{25}) + πn

Combine all the solutions

x = arctan (\frac{4}{25}) + πn

Show solutions in decimal form

x = 0.15865 \dots + πn

cos (θ) + sin (θ) = 1

2 cos (3 x) = - 1

6 sin (\frac{θ}{2}) = - 6 cos (\frac{θ}{2})

csc (θ) = - \frac{4}{3}

9 sin^{2} (θ) + 3 cos (θ) - 9 = - 2

What is the general solution for 100tan(x)-8=50tan(x) ?
The general solution for 100tan(x)-8=50tan(x) is x=0.15865…+pin