What is the general solution for 5tan(y)-1= 1/(5tan(y)) ?

The general solution for 5tan(y)-1= 1/(5tan(y)) is y=0.31297…+pin,y=-0.12298…+pin

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5tan(y)-1= 1/(5tan(y))

5 tan (y) - 1 = \frac{1}{5 tan ( y )}

y = 0.31297 \dots + πn, y = - 0.12298 \dots + πn

Solution steps

5 tan (y) - 1 = \frac{1}{5 tan ( y )}

Solve by substitution

tan (y) = \frac{1 + 5}{10}, tan (y) = \frac{1 - 5}{10}

tan (y) = \frac{1 + 5}{10} : y = arctan (\frac{1 + 5}{10}) + πn

tan (y) = \frac{1 - 5}{10} : y = arctan (\frac{1 - 5}{10}) + πn

Combine all the solutions

y = arctan (\frac{1 + 5}{10}) + πn, y = arctan (\frac{1 - 5}{10}) + πn

Show solutions in decimal form

y = 0.31297 \dots + πn, y = - 0.12298 \dots + πn

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sin (x) = \frac{12}{60}

sin (8 x) = \frac{1}{2}

1 + sin^{2} (x) + cos^{4} (x) = 0

7 \cdot sin^{2} (x) + cos^{2} (x) - 1 = 6 sin (x)

What is the general solution for 5tan(y)-1= 1/(5tan(y)) ?
The general solution for 5tan(y)-1= 1/(5tan(y)) is y=0.31297…+pin,y=-0.12298…+pin