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

The general solution for tan(x)+cot(x)=3 is x=0.36486…+pin,x=1.20593…+pin

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tan(x)+cot(x)=3

tan (x) + cot (x) = 3

x = 0.36486 \dots + πn, x = 1.20593 \dots + πn

Solution steps

tan (x) + cot (x) = 3

Subtract

3

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cot (x) = \frac{3 + 5}{2} : x = arccot (\frac{3 + 5}{2}) + πn

cot (x) = \frac{3 - 5}{2} : x = arccot (\frac{3 - 5}{2}) + πn

Combine all the solutions

x = arccot (\frac{3 + 5}{2}) + πn, x = arccot (\frac{3 - 5}{2}) + πn

Show solutions in decimal form

x = 0.36486 \dots + πn, x = 1.20593 \dots + πn

3 sin (B) - 2 = 5 sin (B) - 1

sin (x) = sin (- x)

3 cos (θ) + 2 = 0

- cot (x) - 3 cos (x) = - cot (x) cos (x) - 3 cos (x)

6 cos^{2} (x) + 3 cos (x) = 0

What is the general solution for tan(x)+cot(x)=3 ?
The general solution for tan(x)+cot(x)=3 is x=0.36486…+pin,x=1.20593…+pin