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

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

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

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

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

Solution steps

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

Subtract

sec (x) + 1

from both sides

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

cos (u) = \frac{2}{5}, cos (2 u)

sin (b) = \frac{2}{2}

h = 7 cos (\frac{π}{3} t), t

3 + 3 sin (θ) = 3 + 3 cos (θ)

- 3 = tan (θ)

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