What is the general solution for sec(2x)+sqrt(2)=0 ?

The general solution for sec(2x)+sqrt(2)=0 is x=(3pi)/8+pin,x=(5pi)/8+pin

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sec(2x)+sqrt(2)=0

sec (2 x) + 2 = 0

x = \frac{3 π}{8} + πn, x = \frac{5 π}{8} + πn

Solution steps

sec (2 x) + 2 = 0

Move

2

to the right side

sec (2 x) = - 2

General solutions for

sec (2 x) = - 2

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

Solve

2 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{8} + πn

Solve

2 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{8} + πn

x = \frac{3 π}{8} + πn, x = \frac{5 π}{8} + πn

3 sin (x + 2 0^{\circ}) - 0.75 = 0

2 sin^{2} (x) + sin (x) - 5 = 0

- 4 sin (x) = 4 (sin (x) - 1)

\frac{3}{tan ( x )} = (2 tan (x)) (2 cos (x))

cos (θ) = - \frac{4}{5}, sin (θ)

What is the general solution for sec(2x)+sqrt(2)=0 ?
The general solution for sec(2x)+sqrt(2)=0 is x=(3pi)/8+pin,x=(5pi)/8+pin