What is the general solution for 2tan(x)-3cot(x)=1 ?

The general solution for 2tan(x)-3cot(x)=1 is x=(3pi)/4+pin,x=0.98279…+pin

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2tan(x)-3cot(x)=1

2 tan (x) - 3 cot (x) = 1

x = \frac{3 π}{4} + πn, x = 0.98279 \dots + πn

Solution steps

2 tan (x) - 3 cot (x) = 1

Subtract

1

from both sides

2 tan (x) - 3 cot (x) - 1 = 0

Rewrite using trig identities

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

Solve by substitution

cot (x) = - 1, cot (x) = \frac{2}{3}

cot (x) = - 1 : x = \frac{3 π}{4} + πn

cot (x) = \frac{2}{3} : x = arccot (\frac{2}{3}) + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = arccot (\frac{2}{3}) + πn

Show solutions in decimal form

x = \frac{3 π}{4} + πn, x = 0.98279 \dots + πn

sin^{2} (x) + cos^{2} (\frac{17}{9}) = 1

8 sin^{2} (x) - 10 sin (x) + 3 = 0

\frac{tan ( x )}{sec ( x )} = cot (x)

2 tan^{2} (x) sin^{2} (x) = 1

cos (7 x) + cos (3 x) = 0

What is the general solution for 2tan(x)-3cot(x)=1 ?
The general solution for 2tan(x)-3cot(x)=1 is x=(3pi)/4+pin,x=0.98279…+pin