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Let sin-1x + ...

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Let sin-1x + sin-1y = sin-1(x√1-y^2 + y√1-x^2) then find the area represented by the locus of point (x,y) if |x|<=1 , |y|<=1

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Q. Prove that :

{sin}^{- 1} x + {sin}^{- 1} y = {sin}^{- 1} [x \sqrt{1 - y^{2}} + y \sqrt{1 - x^{2}}]

{sin}^{- 1} x + {sin}^{- 1} y + {sin}^{- 1} z = π

x \sqrt{1 - x^{2}} + y \sqrt{1 - y^{2}} + z \sqrt{1 - z^{2}} = 2 x y z

Q. Inverse circular functions,Principal values of

{sin}^{- 1} x, {cos}^{- 1} x, {tan}^{- 1} x

.

{tan}^{- 1} x + {tan}^{- 1} y = {tan}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {tan}^{- 1} \frac{x + y}{1 - x y}

x y > 1

{tan}^{- 1} \frac{1 - x}{1 + x} {tan}^{- 1} \frac{1 - y}{1 + y} = {sin}^{- 1} \frac{y - x}{\sqrt{1 + x^{2}} \sqrt{1 + y^{2}}}

- 1 \leq x, y \leq 1

{sin}^{- 1} x + {sin}^{- 1} y = \frac{π}{2},

find the value of

{cos}^{- 1} x + {cos}^{- 1} y .

Q. Prove the following:

s i n^{- 1} x + s i n^{- 1} y + s i n^{- 1} z = π

x \sqrt{1 - x^{2}} + y \sqrt{1 - y^{2}} + z \sqrt{1 - z^{2}} = x y z

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