What is the general solution for 4+tan(x)=5cot(x) ?

The general solution for 4+tan(x)=5cot(x) is x=1.76819…+pin,x= pi/4+pin

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4+tan(x)=5cot(x)

4 + tan (x) = 5 cot (x)

x = 1.76819 \dots + πn, x = \frac{π}{4} + πn

Solution steps

4 + tan (x) = 5 cot (x)

Subtract

5 cot (x)

from both sides

4 + tan (x) - 5 cot (x) = 0

Rewrite using trig identities

4 + \frac{1}{cot ( x )} - 5 cot (x) = 0

Solve by substitution

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

cot (x) = - \frac{1}{5} : x = arccot (- \frac{1}{5}) + πn

cot (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = arccot (- \frac{1}{5}) + πn, x = \frac{π}{4} + πn

Show solutions in decimal form

x = 1.76819 \dots + πn, x = \frac{π}{4} + πn

3 (sin (x) - 2) (4 cos (x) - 2) = 0

\frac{sin ( x )}{120} = \frac{sin ( 8 )}{30}

6 cos (θ) = 0

0.175 = 0.34 sin (93.4 t)

x, cos (x y) - sin (x y) = 2

What is the general solution for 4+tan(x)=5cot(x) ?
The general solution for 4+tan(x)=5cot(x) is x=1.76819…+pin,x= pi/4+pin