What is the general solution for 2cot(x)+sec^2(x)=0 ?

The general solution for 2cot(x)+sec^2(x)=0 is x=(3pi)/4+pin

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2cot(x)+sec^2(x)=0

2 cot (x) + sec^{2} (x) = 0

x = \frac{3 π}{4} + πn

Solution steps

2 cot (x) + sec^{2} (x) = 0

Rewrite using trig identities

1 + \frac{2}{tan ( x )} + tan^{2} (x) = 0

Solve by substitution

tan (x) = - 1, tan (x) = \frac{1}{2} + i \frac{7}{2}, tan (x) = \frac{1}{2} - i \frac{7}{2}

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

tan (x) = \frac{1}{2} + i \frac{7}{2} :

No Solution

tan (x) = \frac{1}{2} - i \frac{7}{2} :

No Solution

Combine all the solutions

x = \frac{3 π}{4} + πn

π cos (θ) = - \frac{π}{2}

x, y = 1 + sin (\frac{π x}{4})

sin (x) + sin (\frac{x}{2}) = 0

sin^{3} (x) + sin (x) = 2 cos^{2} (x)

4 sin^{2} (x) + 2 cos^{2} (x) = 3

What is the general solution for 2cot(x)+sec^2(x)=0 ?
The general solution for 2cot(x)+sec^2(x)=0 is x=(3pi)/4+pin