What is the general solution for tan(2x)=(80}{\frac{30+20)/2} ?

The general solution for tan(2x)=(80}{\frac{30+20)/2} is x=(1.26791…)/2+(pin)/2

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tan(2x)=(80}{\frac{30+20)/2}

tan (2 x) = \frac{80}{\frac{30 + 20}{2}}

x = \frac{1.26791 \dots}{2} + \frac{πn}{2}

Radians

x = \frac{1.26791 \dots}{2} + \frac{π}{2} n

Solution steps

tan (2 x) = \frac{80}{\frac{30 + 20}{2}}

Simplify

\frac{80}{\frac{30 + 20}{2}} : \frac{16}{5}

\frac{80}{\frac{30 + 20}{2}}

Add the numbers:

30 + 20 = 50

= \frac{80}{\frac{50}{2}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{80 \cdot 2}{50}

Multiply the numbers:

80 \cdot 2 = 160

= \frac{160}{50}

Cancel the common factor:

10

= \frac{16}{5}

Apply trig inverse properties

tan (2 x) = \frac{16}{5}

General solutions for

tan (2 x) = \frac{16}{5}

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

2 x = arctan (\frac{16}{5}) + πn

2 x = arctan (\frac{16}{5}) + πn

Solve

2 x = arctan (\frac{16}{5}) + πn : x = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{16}{5}) + πn

Divide both sides by

2

2 x = arctan (\frac{16}{5}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.26791 \dots}{2} + \frac{πn}{2}

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2 sin^{4} (x) = 4 - 7 cos^{2} (x)

4 cos^{2} (A) - 1 = 0

sin (\frac{75 π}{11}) = sin (\frac{x π}{11})

What is the general solution for tan(2x)=(80}{\frac{30+20)/2} ?
The general solution for tan(2x)=(80}{\frac{30+20)/2} is x=(1.26791…)/2+(pin)/2