What is the general solution for 5+3tan(x)=4 ?

The general solution for 5+3tan(x)=4 is x=-0.32175…+pin

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5+3tan(x)=4

5 + 3 tan (x) = 4

x = - 0.32175 \dots + πn

Degrees

x = - 18.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

5 + 3 tan (x) = 4

Move

5

to the right side

5 + 3 tan (x) = 4

Subtract

5

from both sides

5 + 3 tan (x) - 5 = 4 - 5

Simplify

3 tan (x) = - 1

3 tan (x) = - 1

Divide both sides by

3

3 tan (x) = - 1

Divide both sides by

3

\frac{3 tan ( x )}{3} = \frac{- 1}{3}

Simplify

tan (x) = - \frac{1}{3}

tan (x) = - \frac{1}{3}

Apply trig inverse properties

tan (x) = - \frac{1}{3}

General solutions for

tan (x) = - \frac{1}{3}

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

x = arctan (- \frac{1}{3}) + πn

x = arctan (- \frac{1}{3}) + πn

Show solutions in decimal form

x = - 0.32175 \dots + πn

cos (x) + sin (\frac{x}{2}) = 0

4 cos (2 θ) = 8 sin^{2} (θ)

cos (θ) = (\frac{5}{29})

sin (θ) = \frac{7.5}{6.5}

cos^{2} (x) - \frac{3}{2} = \frac{5}{2} cos (x)

What is the general solution for 5+3tan(x)=4 ?
The general solution for 5+3tan(x)=4 is x=-0.32175…+pin