Simplify this pleaseee!?

Question

arc sin (sin x)

the answer must be in terms of x

Answer 1

arc sin (sin x) = x

arc sin is the inverse function of sin.

As such, the two functions together produces a unity function which is f(x) = x

Therefore, arc sin (sin x) = x

Answer 2

Those answers are almost right. Because sin(x) = sin(x+2*pi), the answer is

x + 2*n*pi, n over the range of positive and negative integers.

Answer 3

same way of writing as :
= sin ^ -1(sin x)
= x

note:
the inverse of a number multiplied by the number is always 1

Answer 4

arc sin(sin x) =x

Answer 5

(4y^8 / 9t^3) x (81t^7 / 16y) = (4y^8 x 81t^7) / (9t^3 x 16y) now look for common factors in the denominator and numerator both contain 4y - in the numerator (top), 4y^8 = 4y x y^7, while in the denominator 16y = 4y x 4 both contain 9t^3 - in the numerator, 81t^7 = 9t^3 x 9t^4 pull out the common factors (remember, anything divided by itself equals 1!) what's left is (y^7 x 9t^4) / 4