What is the general solution for 6cot(x)=5-tan(x) ?

The general solution for 6cot(x)=5-tan(x) is x=1.10714…+pin,x=1.24904…+pin

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6cot(x)=5-tan(x)

6 cot (x) = 5 - tan (x)

x = 1.10714 \dots + πn, x = 1.24904 \dots + πn

Solution steps

6 cot (x) = 5 - tan (x)

Subtract

5 - tan (x)

from both sides

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

Rewrite using trig identities

- 5 + \frac{1}{cot ( x )} + 6 cot (x) = 0

Solve by substitution

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

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

cot (x) = \frac{1}{3} : x = arccot (\frac{1}{3}) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 1.10714 \dots + πn, x = 1.24904 \dots + πn

3 cos (θ) - 3 = 0

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

sin (X) = \frac{2}{2}

x, 2 + sin (x) = 0

cosh (\frac{zz}{2}) = 0

What is the general solution for 6cot(x)=5-tan(x) ?
The general solution for 6cot(x)=5-tan(x) is x=1.10714…+pin,x=1.24904…+pin