What is the general solution for tan(x)=5sin(pi/4)sin((3pi)/4) ?

The general solution for tan(x)=5sin(pi/4)sin((3pi)/4) is x=1.19028…+pin

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tan(x)=5sin(pi/4)sin((3pi)/4)

tan (x) = 5 sin (\frac{π}{4}) sin (\frac{3 π}{4})

x = 1.19028 \dots + πn

Solution steps

tan (x) = 5 sin (\frac{π}{4}) sin (\frac{3 π}{4})

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4}) = \frac{2}{2}

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

Simplify

5 \cdot \frac{2}{2} \cdot \frac{2}{2} : \frac{5}{2}

Apply trig inverse properties

x = arctan (\frac{5}{2}) + πn

Show solutions in decimal form

x = 1.19028 \dots + πn

cot (θ) = - \frac{12}{5}

2 - 23 tan (x + \frac{π}{3}) = 0

(cos (x))^{2} = 0

tan (x) = \frac{2}{8}

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

What is the general solution for tan(x)=5sin(pi/4)sin((3pi)/4) ?
The general solution for tan(x)=5sin(pi/4)sin((3pi)/4) is x=1.19028…+pin