What is the general solution for sec^2(θ)+tan(θ)=1 ?

The general solution for sec^2(θ)+tan(θ)=1 is θ=(3pi)/4+pin

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sec^2(θ)+tan(θ)=1

sec^{2} (θ) + tan (θ) = 1

θ = \frac{3 π}{4} + πn

Solution steps

sec^{2} (θ) + tan (θ) = 1

Subtract

1

from both sides

sec^{2} (θ) + tan (θ) - 1 = 0

Rewrite using trig identities

\frac{1}{cot ^{2} ( θ )} + \frac{1}{cot ( θ )} = 0

Solve by substitution

cot (θ) = - 1

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

Combine all the solutions

θ = \frac{3 π}{4} + πn

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

cos (x) + 5 = 5

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

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

3 tan^{2} (x) - 3 tan (x) = 0

What is the general solution for sec^2(θ)+tan(θ)=1 ?
The general solution for sec^2(θ)+tan(θ)=1 is θ=(3pi)/4+pin