Prove that 2tan⁻¹x = sin⁻¹(2x/(1 + x²)) = cos⁻¹((1 - x²)/(1 + x²))

Prove that 2tan-1x = sin-1(2x/(1 + x^2)) = cos-1((1 - x^2)/(1 + x^2))
Show that `2tan^-1x+Sin^-1 (2x)/(1+X^2)`
2tan^-1x+sin^-1(2x/1+x^2) is equal to
2tan^-1x = cos^-1(1-x^2/1+x^2)
if 2 tan^(-1x+sin^(-1)(2x)/(1+x^(2)) is independent of x then
show that 2 tan − 1 x sin − 1 2x 1 x 2 is constant for x ≥ 1
#math #trigonometry