Question

For what values of x is the following formula valid π - 3sin^-1(x) = sin^-1(3x-4x³).

Answer 1

R.H.S

sin^-1 (3x - 4x³)

Putting x = sin θ

= sin^-1 (3 sin θ - 4 sin³ θ)

= sin^-1 (sin 3θ)        (sin 3x = 3 sin x - 4 sin³ x)

= 3θ           (sin^-1(sin x) = x)

Now,

x = sin θ

sin^-1 x = θ

= 3 sin^-1 x

= L.H.S

Hence, proved.