Differentiate the following functions with respect to x:
Let x = a sinθ
Now
Using sin2θ + cos2θ = 1
y = tan–1(tanθ)
Considering the limits,
–a < x < a
–a < asin θ < a
–1 < sin θ < 1
Now, y = tan–1(tanθ)
y = θ
Differentiating w.r.t x, we get