What is the general solution for 1/(sin(x))+1/(cos(x))=0 ?

The general solution for 1/(sin(x))+1/(cos(x))=0 is x=(3pi)/4+pin

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1/(sin(x))+1/(cos(x))=0

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

x = \frac{3 π}{4} + πn

Solution steps

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

Simplify

\frac{1}{sin ( x )} + \frac{1}{cos ( x )} : \frac{cos ( x ) + sin ( x )}{sin ( x ) cos ( x )}

\frac{cos ( x ) + sin ( x )}{sin ( x ) cos ( x )} = 0

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

cos (x) + sin (x) = 0

Rewrite using trig identities

1 + tan (x) = 0

Move

1

to the right side

tan (x) = - 1

General solutions for

tan (x) = - 1

x = \frac{3 π}{4} + πn

1 - cos (2 x) = 0

sin (x) = \frac{37}{64}

1 = 4 tan (- \frac{4}{81} + c)

15 cos^{2} (x) + 7 cos (x) - 2 = 0

2 (sin (t))^{2} - sin (t) - 1 = 0

What is the general solution for 1/(sin(x))+1/(cos(x))=0 ?
The general solution for 1/(sin(x))+1/(cos(x))=0 is x=(3pi)/4+pin