What is the general solution for sec^2(x)+tan(x)-1=0 ?

The general solution for sec^2(x)+tan(x)-1=0 is x=(3pi)/4+pin

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sec^2(x)+tan(x)-1=0

sec^{2} (x) + tan (x) - 1 = 0

x = \frac{3 π}{4} + πn

Solution steps

sec^{2} (x) + tan (x) - 1 = 0

Rewrite using trig identities

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

Solve by substitution

cot (x) = - 1

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

Combine all the solutions

x = \frac{3 π}{4} + πn

0 = sin (θ)

6 tan^{4} (x) - tan^{2} (x) - 2 = 0

t, x = sin (t)

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

2 tan^{2} (x) = 13

What is the general solution for sec^2(x)+tan(x)-1=0 ?
The general solution for sec^2(x)+tan(x)-1=0 is x=(3pi)/4+pin