What is the general solution for 6/(3tan(θ)+1)=5 ?

The general solution for 6/(3tan(θ)+1)=5 is θ=0.06656…+pin

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6/(3tan(θ)+1)=5

\frac{6}{3 tan ( θ ) + 1} = 5

θ = 0.06656 \dots + πn

Solution steps

\frac{6}{3 tan ( θ ) + 1} = 5

Multiply both sides by

3 tan (θ) + 1

6 = 5 (3 tan (θ) + 1)

Switch sides

5 (3 tan (θ) + 1) = 6

Divide both sides by

5

3 tan (θ) + 1 = \frac{6}{5}

Move

1

to the right side

3 tan (θ) = \frac{1}{5}

Divide both sides by

3

tan (θ) = \frac{1}{15}

Verify Solutions

Find undefined (singularity) points:

tan (θ) = - \frac{1}{3}

Combine undefined points with solutions:

tan (θ) = \frac{1}{15}

Apply trig inverse properties

θ = arctan (\frac{1}{15}) + πn

Show solutions in decimal form

θ = 0.06656 \dots + πn

cos (x) = 2 - 3 sin (x)

tan (\frac{x}{2}) = 1, 5

2 cos^{2} (x) - 1 - cos (x) = 0, 0 \leq x \leq 2 π

cos (θ) = \frac{- 3}{5}

tan^{2} (x) - tan (x) = 2

What is the general solution for 6/(3tan(θ)+1)=5 ?
The general solution for 6/(3tan(θ)+1)=5 is θ=0.06656…+pin