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

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

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sec^2(x)=2

sec^{2} (x) = 2

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) = 2

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

sinh (3 x) - 3 sinh (x) = 0

cos (4 x) = sin (2 x)

csc (θ) = 2

- sin (x) - cos (x) = 0

sec (x) sin (x) - 2 sin (x) = 0

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