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

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

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sec^2(θ)=1-tan(θ)

sec^{2} (θ) = 1 - tan (θ)

θ = \frac{3 π}{4} + πn

Solution steps

sec^{2} (θ) = 1 - tan (θ)

Subtract

1 - tan (θ)

from both sides

sec^{2} (θ) - 1 + tan (θ) = 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^{2} (x) = - 0.267

sin (x - 4) = cos (9 x + 4)

x, 0 = - 2 sin (x) - 4 cos (2 x)

tan (a) = \frac{4}{4}

cos^{2} (θ) = 2 cos (θ)

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