What is the general solution for sec^4(x)-4=0 ?

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

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sec^4(x)-4=0

sec^{4} (x) - 4 = 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

sec^{4} (x) - 4 = 0

Solve by substitution

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

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

sec (x) = 2 i :

No Solution

sec (x) = - 2 i :

No Solution

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^{2} (θ) - 1 = 0, 0 \leq θ \leq 2 π

cos (3 θ) = \frac{3}{2}

tan^{2} (θ) - 1 = 0, π \leq θ \leq 2 π

sin (y) = - \frac{1}{2}

cos^{22} (x) - 2 sin^{2} (x) - 1 = 0

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