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

The general solution for tan^2(x)=1+sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

Solution steps

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

Subtract

1 + sec (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sec (x) = 2, sec (x) = - 1

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

8 sin^{2} (x) = 7

- 6 arcsin (3 x) = π

tan^{2} (p) = tan (p)

sin (x) + cos (x) = \frac{2}{3}

2 cos^{2} (2 θ) = 1 - cos (2 θ)

What is the general solution for tan^2(x)=1+sec(x) ?
The general solution for tan^2(x)=1+sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin