What is the general solution for 2tan(x)-3cot(x)=0 ?

The general solution for 2tan(x)-3cot(x)=0 is x=0.88607…+pin,x=2.25551…+pin

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

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

x = 0.88607 \dots + πn, x = 2.25551 \dots + πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

x = 0.88607 \dots + πn, x = 2.25551 \dots + πn

8 sin (2 x) + 15 cos (x) = 0

cos (\frac{x}{2}) - 2 cos (x) - 2 = 0

8 \cdot cos^{2} (3 x) + 6 \cdot cos (6 x) = 10216

sin (x) = \frac{48 \cdot sin ( 6 9 ^{\circ} )}{47.5}

cos (x) = \frac{8 3}{16}

What is the general solution for 2tan(x)-3cot(x)=0 ?
The general solution for 2tan(x)-3cot(x)=0 is x=0.88607…+pin,x=2.25551…+pin