Prove that 2tan-1x - sin-12x1 - x2

y=sin^ 1 ( 2x1+x^2 ) Let #160; x=tanθ y=sin^ 1 ( 2tanθ1+tan^2θ ) y=sin^ 1 ( sin 2θ #160; ) y=2θ y=2tan^ 1x ...

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Trigonometric Ratio(sin,cos,tan)

Prove that ...

Question

Prove that $2 t a n^{- 1} x = s i n^{- 1} (\frac{2 x}{1 + x^{2}})$

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(1) {sin}^{- 1} (\frac{2 x}{1 + x^{2}}) = 2 {tan}^{- 1} x, | x | \leq 1

(2) {cos}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) = 2 {tan}^{- 1} x, x \geq 0

(3) {tan}^{- 1} (\frac{2 x}{1 - x^{2}}) = 2 {tan}^{- 1} x, - 1 < x < 1

2 {tan}^{- 1} x = {tan}^{- 1} \frac{2 x}{1 - x^{2}}

{sin}^{- 1} \frac{2 x}{1 + x^{2}}; {cos}^{- 1} \frac{1 - x^{2}}{1 + x^{2}}; {tan}^{- 1} \frac{2 x}{1 - x^{2}} .

2 {tan}^{- 1} x .

\int 2 {tan}^{- 1} x = 2 [x {tan}^{- 1} x - \frac{1}{2} log (1 + x^{2})]

2 t a n^{- 1} x = s i n^{- 1} \frac{2 x}{1 + x^{2}}

f (x) = 2 {tan}^{- 1} x + {sin}^{- 1} \frac{2 x}{1 + x^{2}}

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