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= pi/4+pin,x=pin

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

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

x = \frac{π}{4} + πn, x = πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = 1, tan (x) = 0

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = 0 : x = πn

Combine all the solutions

x = \frac{π}{4} + πn, x = πn

2 cos (2 x + \frac{π}{6}) + 3 = 2, 0 < x < 2 π

cos (x) - 3 sin (x) = 2

(cot (θ) + 3) (csc (θ) + 2) = 0

cos (x) = \frac{- 2}{5}

sin (\frac{θ}{2}) = \frac{1}{m}

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= pi/4+pin,x=pin