What is the general solution for csc^2(x)+2cot^2(x)=1 ?

The general solution for csc^2(x)+2cot^2(x)=1 is x= pi/2+pin

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csc^2(x)+2cot^2(x)=1

csc^{2} (x) + 2 cot^{2} (x) = 1

x = \frac{π}{2} + πn

Solution steps

csc^{2} (x) + 2 cot^{2} (x) = 1

Subtract

1

from both sides

csc^{2} (x) + 2 cot^{2} (x) - 1 = 0

Rewrite using trig identities

3 cot^{2} (x) = 0

Divide both sides by

3

cot (x) = 0

General solutions for

cot (x) = 0

x = \frac{π}{2} + πn

3 csc (2 x) + 2 = 0

x, 2 cos^{2} (x) - 1 = 0

- 25 sin (5 x) = 0

6 sin^{2} (x) - sin (x) - 1 = 0

sin (x) = \frac{9}{11}

What is the general solution for csc^2(x)+2cot^2(x)=1 ?
The general solution for csc^2(x)+2cot^2(x)=1 is x= pi/2+pin