What is the general solution for (2*40)/(80+20)=tan(2x) ?

The general solution for (2*40)/(80+20)=tan(2x) is x=(0.67474…)/2+(pin)/2

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(2*40)/(80+20)=tan(2x)

\frac{2 \cdot 40}{80 + 20} = tan (2 x)

x = \frac{0.67474 \dots}{2} + \frac{πn}{2}

Degrees

x = 19.32990 \dots^{\circ} + 9 0^{\circ} n

Solution steps

\frac{2 \cdot 40}{80 + 20} = tan (2 x)

Switch sides

tan (2 x) = \frac{2 \cdot 40}{80 + 20}

Simplify

\frac{2 \cdot 40}{80 + 20} : \frac{4}{5}

\frac{2 \cdot 40}{80 + 20}

Multiply the numbers:

2 \cdot 40 = 80

= \frac{80}{80 + 20}

Add the numbers:

80 + 20 = 100

= \frac{80}{100}

Cancel the common factor:

20

= \frac{4}{5}

Apply trig inverse properties

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

General solutions for

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

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

2 x = arctan (\frac{4}{5}) + πn

2 x = arctan (\frac{4}{5}) + πn

Solve

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

2 x = arctan (\frac{4}{5}) + πn

Divide both sides by

2

2 x = arctan (\frac{4}{5}) + πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.67474 \dots}{2} + \frac{πn}{2}

x, sec (x + 1 0^{\circ}) = 5.759

tan (x) cot (x) + 2 cot (x) = 0

2 \cdot cos^{2} (x) + cos (x) = 0

- cos^{2} (θ) + sin^{2} (θ) = 0

sin (A) = \frac{( 5.4 ) ( sin ( 3 3 ^{\circ} ) )}{6.7}

What is the general solution for (2*40)/(80+20)=tan(2x) ?
The general solution for (2*40)/(80+20)=tan(2x) is x=(0.67474…)/2+(pin)/2