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

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

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csc(x)sec(x)=2sqrt(2)

csc (x) sec (x) = 22

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

Solution steps

csc (x) sec (x) = 22

Subtract

22

from both sides

csc (x) sec (x) - 22 = 0

Express with sin, cos

\frac{1 - 2 cos ( x ) sin ( x ) 2}{cos ( x ) sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 - 2 cos (x) sin (x) 2 = 0

Rewrite using trig identities

1 - sin (2 x) 2 = 0

Move

1

to the right side

- sin (2 x) 2 = - 1

Divide both sides by

- 2

sin (2 x) = \frac{2}{2}

General solutions for

sin (2 x) = \frac{2}{2}

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

Solve

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

Solve

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

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

u, x = sinh (u)

sin (θ) = \frac{tan ( θ )}{sin ( θ )}

5 tan^{2} (t) - tan (t) = 0

sin (x) = \frac{9}{16}

24 = 32 + 8 - 2 \cdot 32 \cdot 8 \cdot cos (θ)

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