What is the general solution for 5cot(x)+2csc^2(x)=5 ?

The general solution for 5cot(x)+2csc^2(x)=5 is x=1.10714…+pin,x=2.81984…+pin

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5cot(x)+2csc^2(x)=5

5 cot (x) + 2 csc^{2} (x) = 5

x = 1.10714 \dots + πn, x = 2.81984 \dots + πn

Solution steps

5 cot (x) + 2 csc^{2} (x) = 5

Subtract

5

from both sides

5 cot (x) + 2 csc^{2} (x) - 5 = 0

Rewrite using trig identities

- 3 + 2 cot^{2} (x) + 5 cot (x) = 0

Solve by substitution

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

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

cot (x) = - 3 : x = arccot (- 3) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 1.10714 \dots + πn, x = 2.81984 \dots + πn

cos (2 x) = \frac{4}{5}

tan (x) = \frac{160}{85}

sin (x) a = π

sin (5 x) + sin (x) = 0

cot^{2} (x) + csc^{2} (x) = 3

What is the general solution for 5cot(x)+2csc^2(x)=5 ?
The general solution for 5cot(x)+2csc^2(x)=5 is x=1.10714…+pin,x=2.81984…+pin