The inverse Trigonometric Functions are partial inverse Functions for every trigonometric function. The sine Inverse Function is also said to be inverse sine (sin-1) or arcsine (arcsin).
This sine function also satisfies some conditions which are given below:
1. Sin (arcsin p) = p for every value | p | ≤ 1;
2. arcsin (sin p) = p for every value | p | ≤ ⊼ / 2 + k⊼;
Now we will see the representation of inverse trigonometric function:
Now we will see how to differentiate sin inverse;
Let, y = sin-1(x).
then, x = sin(y) and dx/dy = cos(y)
dy/dx = 1/cos(y)
dy/dx = 1/√(1 - x^2)