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

The general solution for (csc(x))/(cot(x))=sqrt(2) is x= pi/4+2pin,x=(7pi)/4+2pin

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(csc(x))/(cot(x))=sqrt(2)

\frac{csc ( x )}{cot ( x )} = 2

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

\frac{csc ( x )}{cot ( x )} = 2

Subtract

2

from both sides

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

Simplify

\frac{csc ( x )}{cot ( x )} - 2 : \frac{csc ( x ) - 2 cot ( x )}{cot ( x )}

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

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

csc (x) - 2 cot (x) = 0

Express with sin, cos

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

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

1 - cos (x) 2 = 0

Move

1

to the right side

- cos (x) 2 = - 1

Divide both sides by

- 2

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

General solutions for

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

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sin (4 x) + 6 cos (2 x) = 0

sec (θ) + tan (θ) = 0

sin (θ) = \frac{3.5}{5}

sec (a) = \frac{41}{12}, 2 π < a < \frac{5 π}{2}, sin (\frac{a}{2})

sin (2 x) = 0.3

What is the general solution for (csc(x))/(cot(x))=sqrt(2) ?
The general solution for (csc(x))/(cot(x))=sqrt(2) is x= pi/4+2pin,x=(7pi)/4+2pin