What is the general solution for 5=sec^2(x)+3 ?

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

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5=sec^2(x)+3

5 = sec^{2} (x) + 3

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

5 = sec^{2} (x) + 3

Switch sides

sec^{2} (x) + 3 = 5

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 (θ) = \frac{24}{25}

sin (2 t) = cos (t)

cos (2 x) + 1 = cos (x)

4 cos (x) + 1 = 0

2 cot^{2} (x) + csc^{2} (x) - 2 = 0

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