What is the general solution for 7sec^2(x)-7sec(x)=14 ?

The general solution for 7sec^2(x)-7sec(x)=14 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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7sec^2(x)-7sec(x)=14

7 sec^{2} (x) - 7 sec (x) = 14

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

Solution steps

7 sec^{2} (x) - 7 sec (x) = 14

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

0 = 1 + 2 sin (2 x)

0 = 1 + 2 cos (3 θ)

tan (4 x) = - 3

sin (π x) = - \frac{1}{2}

cos^{2} (x) + sin (x) - 1 = 0

What is the general solution for 7sec^2(x)-7sec(x)=14 ?
The general solution for 7sec^2(x)-7sec(x)=14 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin