What is the general solution for 1/(sin(x)cos(x))=2sqrt(2) ?

The general solution for 1/(sin(x)cos(x))=2sqrt(2) is x= pi/8+pin,x=(3pi)/8+pin

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1/(sin(x)cos(x))=2sqrt(2)

\frac{1}{sin ( x ) cos ( x )} = 22

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

Solution steps

\frac{1}{sin ( x ) cos ( x )} = 22

Rewrite using trig identities

\frac{1}{\frac{s i n ( 2 x )}{2}} = 22

Simplify

\frac{1}{\frac{s i n ( 2 x )}{2}} : \frac{2}{sin ( 2 x )}

\frac{2}{sin ( 2 x )} = 22

Multiply both sides by

sin (2 x)

2 = 22 sin (2 x)

Switch sides

22 sin (2 x) = 2

Divide both sides by

22

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

Verify Solutions

Find undefined (singularity) points:

sin (2 x) = 0

Combine undefined points with solutions:

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

tan (x) = \frac{1}{5 ^{\frac{1}{2}}}

3 csc (\frac{x}{2}) - 2 = 0

arcsin (y) = \frac{1}{2}

6 sin (y) = 0

tan (θ) = - \frac{3}{3}, 0 \leq θ \leq 2 π

What is the general solution for 1/(sin(x)cos(x))=2sqrt(2) ?
The general solution for 1/(sin(x)cos(x))=2sqrt(2) is x= pi/8+pin,x=(3pi)/8+pin