Solve trigonometric equation

Question

Tan^-1 2x = sin^-1x

please give exact answers

Answer 1

Bianca

 

tan^-12x = sin^-1x

 

We can say that 

 

tan θ = 2x

sin θ = x

 

tan θ = sin θ / cos θ 

 

sin θ / cos θ = 2x

sin θ = x

 

Using substitution

x / cos θ = 2x

1/cos θ = 2

cos θ = 1/2

θ = 60° = π/3

 

Going back to the original problem

tan^-12x = sin^-1x = π/3

 

sin π/3 = √3/2 = x

 

x = 0.866