What is the general solution for 3tan(x)-2cot(x)=5 ?

The general solution for 3tan(x)-2cot(x)=5 is x=2.81984…+pin,x=1.10714…+pin

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3tan(x)-2cot(x)=5

3 tan (x) - 2 cot (x) = 5

x = 2.81984 \dots + πn, x = 1.10714 \dots + πn

Solution steps

3 tan (x) - 2 cot (x) = 5

Subtract

5

from both sides

3 tan (x) - 2 cot (x) - 5 = 0

Rewrite using trig identities

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

Solve by substitution

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

cot (x) = - 3 : x = arccot (- 3) + πn

cot (x) = \frac{1}{2} : x = arccot (\frac{1}{2}) + πn

Combine all the solutions

x = arccot (- 3) + πn, x = arccot (\frac{1}{2}) + πn

Show solutions in decimal form

x = 2.81984 \dots + πn, x = 1.10714 \dots + πn

tan (θ) = \frac{\frac{3}{1} - \frac{2}{5}}{1 + \frac{3}{1} \cdot \frac{2}{5}}

tan (t) = 14

cos (A) = \frac{5}{8}

sin (9 x + 40) = cos (- 5 x + 42)

sin^{2} (a) = - \frac{( 5 11 )}{( 18 )}

What is the general solution for 3tan(x)-2cot(x)=5 ?
The general solution for 3tan(x)-2cot(x)=5 is x=2.81984…+pin,x=1.10714…+pin