What is the general solution for sec^2(θ)+2tan(θ)=0 ?

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

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sec^2(θ)+2tan(θ)=0

sec^{2} (θ) + 2 tan (θ) = 0

θ = \frac{3 π}{4} + πn

Solution steps

sec^{2} (θ) + 2 tan (θ) = 0

Rewrite using trig identities

1 + tan^{2} (θ) + 2 tan (θ) = 0

Solve by substitution

tan (θ) = - 1

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

Combine all the solutions

θ = \frac{3 π}{4} + πn

4 sin^{2} (\frac{x}{2}) + 8 cos (\frac{x}{2}) - 7 = 0

sin (x) + cos (x) = 1, - 36 0^{\circ} \leq x \leq 36 0^{\circ}

5 csc (θ) + 6 = 0

sin (x^{2}) = 1

cos (2 θ) - 3 cos (θ) = 0, 0 \leq θ < 2 π

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