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

The general solution for tan(x)+cot(x)=5 is x=0.20575…+pin,x=1.36503…+pin

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tan(x)+cot(x)=5

tan (x) + cot (x) = 5

x = 0.20575 \dots + πn, x = 1.36503 \dots + πn

Solution steps

tan (x) + cot (x) = 5

Subtract

5

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cot (x) = \frac{5 + 21}{2}, cot (x) = \frac{5 - 21}{2}

cot (x) = \frac{5 + 21}{2} : x = arccot (\frac{5 + 21}{2}) + πn

cot (x) = \frac{5 - 21}{2} : x = arccot (\frac{5 - 21}{2}) + πn

Combine all the solutions

x = arccot (\frac{5 + 21}{2}) + πn, x = arccot (\frac{5 - 21}{2}) + πn

Show solutions in decimal form

x = 0.20575 \dots + πn, x = 1.36503 \dots + πn

5 sin^{2} (θ) + 12 sin (θ) + 7 = 0

3 sin (x) + 2 sin^{2} (x) = - 1

(tan (x) + 3) (2 sin (x) - 2) = 0

3 cos^{2} (x) - 2 cos (x) - 2 = 0, 0 \leq x < 2 π

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) + \frac{6}{2} = 0

What is the general solution for tan(x)+cot(x)=5 ?
The general solution for tan(x)+cot(x)=5 is x=0.20575…+pin,x=1.36503…+pin