What is the general solution for 6=2+5arctan(x/2) ?

The general solution for 6=2+5arctan(x/2) is x=2tan(4/5)

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6=2+5arctan(x/2)

6 = 2 + 5 arctan (\frac{x}{2})

x = 2 tan (\frac{4}{5})

Solution steps

6 = 2 + 5 arctan (\frac{x}{2})

Switch sides

2 + 5 arctan (\frac{x}{2}) = 6

Move

2

to the right side

2 + 5 arctan (\frac{x}{2}) = 6

Subtract

2

from both sides

2 + 5 arctan (\frac{x}{2}) - 2 = 6 - 2

Simplify

5 arctan (\frac{x}{2}) = 4

5 arctan (\frac{x}{2}) = 4

Divide both sides by

5

5 arctan (\frac{x}{2}) = 4

Divide both sides by

5

\frac{5 arctan ( \frac{x}{2} )}{5} = \frac{4}{5}

Simplify

arctan (\frac{x}{2}) = \frac{4}{5}

arctan (\frac{x}{2}) = \frac{4}{5}

Apply trig inverse properties

arctan (\frac{x}{2}) = \frac{4}{5}

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

\frac{x}{2} = tan (\frac{4}{5})

\frac{x}{2} = tan (\frac{4}{5})

Solve

\frac{x}{2} = tan (\frac{4}{5}) : x = 2 tan (\frac{4}{5})

\frac{x}{2} = tan (\frac{4}{5})

Multiply both sides by

2

\frac{x}{2} = tan (\frac{4}{5})

Multiply both sides by

2

\frac{2 x}{2} = 2 tan (\frac{4}{5})

Simplify

x = 2 tan (\frac{4}{5})

x = 2 tan (\frac{4}{5})

x = 2 tan (\frac{4}{5})

tan^{2} (θ) - 2 sec (θ) = 2

- sin (B) - 4 = 3 sin (B) - 5

cos^{2} (x) - 7 cos (x) - 1 = 0

sec^{2} (x) + tan (x) - 1 = 0

0 = sin (θ)

What is the general solution for 6=2+5arctan(x/2) ?
The general solution for 6=2+5arctan(x/2) is x=2tan(4/5)