Write each of the following in the simplest form:
Put x = cos θ
= sin–1(2tan–1)
1 – cosθ = 2 sin2 and 1 + cos θ = 2 cos2
= sin–1(2tan–1)
= sin–1(2tan–1)
= sin–1(2tan–1(tan))
= sin–1()
= sin–1(θ)
But θ = cos–1x
∴ The above expression becomes sin–1(cos–1x)