What is the general solution for csc^2(x)=3cot(x)+5 ?

The general solution for csc^2(x)=3cot(x)+5 is x=0.24497…+pin,x=(3pi)/4+pin

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csc^2(x)=3cot(x)+5

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

x = 0.24497 \dots + πn, x = \frac{3 π}{4} + πn

Solution steps

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

Subtract

3 cot (x) + 5

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cot (x) = 4 : x = arccot (4) + πn

cot (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = arccot (4) + πn, x = \frac{3 π}{4} + πn

Show solutions in decimal form

x = 0.24497 \dots + πn, x = \frac{3 π}{4} + πn

7^{2} + 2 5^{2} - 2 (7) (25) cos (x) = 2 4^{2}

tan (x) = 0.015

x, - sin (2 x) = 0

- 2 sin (x) - 2 sin (x) cos (x) = 0

6 cos^{2} (x) + 5 cos (x) + 1 = 0

What is the general solution for csc^2(x)=3cot(x)+5 ?
The general solution for csc^2(x)=3cot(x)+5 is x=0.24497…+pin,x=(3pi)/4+pin