What is the general solution for 7tan(x)=3sqrt(3)+tan(x) ?

The general solution for 7tan(x)=3sqrt(3)+tan(x) is x=0.71372…+pin

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7tan(x)=3sqrt(3)+tan(x)

7 tan (x) = 33 + tan (x)

x = 0.71372 \dots + πn

Degrees

x = 40.89339 \dots^{\circ} + 18 0^{\circ} n

Solution steps

7 tan (x) = 33 + tan (x)

Solve by substitution

7 tan (x) = 33 + tan (x)

Let:

tan (x) = u

7 u = 33 + u

7 u = 33 + u : u = \frac{3}{2}

7 u = 33 + u

Move

u

to the left side

7 u = 33 + u

Subtract

u

from both sides

7 u - u = 33 + u - u

Simplify

6 u = 33

6 u = 33

Divide both sides by

6

6 u = 33

Divide both sides by

6

\frac{6 u}{6} = \frac{3 3}{6}

Simplify

u = \frac{3}{2}

u = \frac{3}{2}

Substitute back

u = tan (x)

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

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (\frac{3}{2}) + πn

x = arctan (\frac{3}{2}) + πn

Combine all the solutions

x = arctan (\frac{3}{2}) + πn

Show solutions in decimal form

x = 0.71372 \dots + πn

cos (2 x) = tan (2 x)

sin (\frac{θ}{2}) - 1 = 0

2 sin (4 x) + 3 = 0

7 sec (x) + 7 tan (x) = 7

sin (2 x) = - 2 sin (x)

What is the general solution for 7tan(x)=3sqrt(3)+tan(x) ?
The general solution for 7tan(x)=3sqrt(3)+tan(x) is x=0.71372…+pin