Question

True or false There is no solution to the equation csc x = -1.

Answer 1

Answer:

The statement is false because the equation has solutions.

Step-by-step explanation:

Given the statement that the equation $\csc x = - 1$, has no solution.

The statement is false because the equation has a definite solution.

Now, $\csc x = - 1$

⇒ $\sin x = \frac{1}{- 1} = - 1$ {Since we know that  $\sin x = \frac{1}{\csc x}$ }

⇒ $x = \sin ^{- 1}(- 1)$

⇒ $x = \frac{3\pi }{2}$ (Answer)