What is the general solution for 3sec^2(x)-6=0 ?

The general solution for 3sec^2(x)-6=0 is x= pi/4+2pin,x=(7pi)/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin

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3sec^2(x)-6=0

3 sec^{2} (x) - 6 = 0

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

3 sec^{2} (x) - 6 = 0

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

sin (x) = \frac{6}{19}

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

4 sin^{2} (x) - 4 cos^{2} (x) = 23

sec^{2} (θ) = 1

cos (\frac{x + π}{2}) = sin (x)

What is the general solution for 3sec^2(x)-6=0 ?
The general solution for 3sec^2(x)-6=0 is x= pi/4+2pin,x=(7pi)/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin