What is the general solution for 5tan(x)=15cot(x) ?

The general solution for 5tan(x)=15cot(x) is x=1.04719…+pin,x=2.09439…+pin

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5tan(x)=15cot(x)

5 tan (x) = 15 cot (x)

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

Solution steps

5 tan (x) = 15 cot (x)

Subtract

15 cot (x)

from both sides

5 tan (x) - 15 cot (x) = 0

Rewrite using trig identities

\frac{5}{cot ( x )} - 15 cot (x) = 0

Solve by substitution

cot (x) = \frac{1}{3}, cot (x) = - \frac{1}{3}

cot (x) = \frac{1}{3} : x = arccot (\frac{1}{3}) + πn

cot (x) = - \frac{1}{3} : x = arccot (- \frac{1}{3}) + πn

Combine all the solutions

x = arccot (\frac{1}{3}) + πn, x = arccot (- \frac{1}{3}) + πn

Show solutions in decimal form

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

x, arctan (x) = arctan (y)

2 cos (x) - 23 \cdot sin (x) = 8

\frac{( cot ( x ) - 3 )}{( 2 sin ( x ) + 1 )} = 0

sin^{2} (x) + 3 sin (x) - 1 = 0

tan (x) - 3^{\frac{1}{2}} = 0

What is the general solution for 5tan(x)=15cot(x) ?
The general solution for 5tan(x)=15cot(x) is x=1.04719…+pin,x=2.09439…+pin