What is the general solution for cos(a)= 1/(sin(a)) ?

The general solution for cos(a)= 1/(sin(a)) is No Solution for a\in\mathbb{R}

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cos(a)= 1/(sin(a))

cos (a) = \frac{1}{sin ( a )}

No Solution for a \in R

Solution steps

cos (a) = \frac{1}{sin ( a )}

Subtract

\frac{1}{sin ( a )}

from both sides

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

Simplify

cos (a) - \frac{1}{sin ( a )} : \frac{cos ( a ) sin ( a ) - 1}{sin ( a )}

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

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

cos (a) sin (a) - 1 = 0

Rewrite using trig identities

- 1 + \frac{sin ( 2 a )}{2} = 0

Move

1

to the right side

\frac{sin ( 2 a )}{2} = 1

Multiply both sides by

2

sin (2 a) = 2

- 1 \leq sin (x) \leq 1

No Solution for a \in R

sin (a) = cos (a)

tan (a) = 2.0503

4 sin (x) = 3 csc (x) - 4

5 sin (θ) - 3 = 0

arctan (1 + x^{2}) = 0

What is the general solution for cos(a)= 1/(sin(a)) ?
The general solution for cos(a)= 1/(sin(a)) is No Solution for a\in\mathbb{R}