Which of the following expressions are identical?
a. (sinx)^-1
b. arcsinx
c. sin x^-1
d. 1/sinx
To determine which of the expressions are identical, we need to understand the notation used and the corresponding trigonometric function.
a. (sinx)^-1: This expression represents the inverse of the sine function. It does NOT represent the reciprocal of the sine function.
b. arcsinx: This expression represents the inverse sine function. It is equivalent to finding the angle (in radians or degrees) whose sine value is given.
c. sin x^-1: This expression represents the reciprocal of the sine function. It is equivalent to 1/sinx.
d. 1/sinx: This expression also represents the reciprocal of the sine function. It is the same as sin x^-1.
In summary, expressions (c) sin x^-1 and (d) 1/sinx are identical and represent the reciprocal of the sine function. So the answer is c and d.