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

The general solution for 4tan(x)+cot(x)=5 is x=0.24497…+pin,x= pi/4+pin

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

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

x = 0.24497 \dots + πn, x = \frac{π}{4} + πn

Solution steps

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

Subtract

5

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cot (x) = 4, cot (x) = 1

cot (x) = 4 : x = arccot (4) + πn

cot (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.24497 \dots + πn, x = \frac{π}{4} + πn

75 = arcsin (\frac{1.4}{x})

tan (2 x + 60) = 33

cos (\frac{π}{3} + x) = sin (3 0^{\circ} - x)

2 cos^{2} (x) + cos (x) = cos (2 x)

tan (x) - tan (\frac{π}{18}) = 1 + tan (x) tan (\frac{π}{18})

What is the general solution for 4tan(x)+cot(x)=5 ?
The general solution for 4tan(x)+cot(x)=5 is x=0.24497…+pin,x= pi/4+pin