Final Answer:
Yes,−csc(y) the same as [−1 / sin(y)], thus the correct option is A.
Step-by-step explanation:
The expression csc(y) is the reciprocal of the expression sin(y), which can be written as 1/sin(y). Thus, when csc(y) is multiplied by -1, the result is -1/sin(y), which is the same as -csc(y). To further understand this concept, let us consider an example. Suppose that y = π/4. Then, sin(y) = sin(π/4) = √2/2. This means that csc(y) = 1/√2/2 = 2/√2. Since -1 multiplied by 2/√2 is equal to -2/√2, this means that -csc(y) = -2/√2 = -1/sin(y).
This example shows that -csc(y) and -1/sin(y) are equivalent expressions and, therefore, the answer to the given question is yes. Moreover, it is important to note that the expression -1/sin(y) can be used to express the same concept as -csc(y) in a simpler way. This is because -1/sin(y) is a fraction with a negative sign in the numerator, while -csc(y) is a trigonometric expression. Thus, -1/sin(y) is a simpler expression than -csc(y).
In conclusion, the answer to the given question is yes, as -csc(y) and -1/sin(y) are equivalent expressions. This can be seen through an example, as well as the fact that -1/sin(y) is a simpler expression than -csc(y).