What is the general solution for sec^2(x)-6=-4 ?

The general solution for sec^2(x)-6=-4 is x= pi/4+2pin,x=(7pi)/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin

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sec^2(x)-6=-4

sec^{2} (x) - 6 = - 4

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Solution steps

sec^{2} (x) - 6 = - 4

Solve by substitution

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

sec (x) = 2 : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sec (x) = - 2 : x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

2 sin (x) = \frac{1}{sin ( x )}

tan (x) - tan (2 x) = 0

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

cos (2 x) - 7 cos (x) + 4 = 0

\frac{87.17}{sin ( 12 0 ^{\circ} )} = \frac{40}{sin ( x )}

What is the general solution for sec^2(x)-6=-4 ?
The general solution for sec^2(x)-6=-4 is x= pi/4+2pin,x=(7pi)/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin