Question

3cos^-1x = cos^-1(4x³ – 3x), x ∈ [\(\frac { 1 }{ 2 }\), 1]
 

Answer 1

Let cos^-1x = θ.
cos θ = x.
Now, cos 3θ = 4cos³θ – 3 cos θ = 4x³ – 3x.
or 3θ = cos^-1(4x³ – 3x)
or 3 cos^-1x = cos^-1(4x³ – 3x), x ∈ [- \(\frac { 1 }{ 2 }\), 1]