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}

Solution steps

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

Simplify

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

Apply trig inverse properties

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}

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