What is the general solution for 5cot(x)+3tan(x)=8 ?

The general solution for 5cot(x)+3tan(x)=8 is x= pi/4+pin,x=1.03037…+pin

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5cot(x)+3tan(x)=8

5 cot (x) + 3 tan (x) = 8

x = \frac{π}{4} + πn, x = 1.03037 \dots + πn

Solution steps

5 cot (x) + 3 tan (x) = 8

Subtract

8

from both sides

5 cot (x) + 3 tan (x) - 8 = 0

Rewrite using trig identities

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

Solve by substitution

cot (x) = 1, cot (x) = \frac{3}{5}

cot (x) = 1 : x = \frac{π}{4} + πn

cot (x) = \frac{3}{5} : x = arccot (\frac{3}{5}) + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = arccot (\frac{3}{5}) + πn

Show solutions in decimal form

x = \frac{π}{4} + πn, x = 1.03037 \dots + πn

sin (2 x) - 1 = cos (2 x), \forall 0 \leq θ < 2 π

tan (θ) = \frac{14}{20}

2 cos^{2} (2 θ) + sin (2 θ) = 1, - 18 0^{\circ} \leq θ \leq 18 0^{\circ}

3 cos (4 x) - 2 = \frac{3}{2} sin (8 x) - 2

4 \cdot cos (x) sin (x) + 3 \cdot cos (x) = 0

What is the general solution for 5cot(x)+3tan(x)=8 ?
The general solution for 5cot(x)+3tan(x)=8 is x= pi/4+pin,x=1.03037…+pin