- #1

utkarshakash

Gold Member

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- 13

## Homework Statement

If [itex]sin^{-1}x+sin^{-1}y+sin^{-1}z = \pi [/itex] then prove that [itex]x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz [/itex]

## Homework Equations

## The Attempt at a Solution

I assume the inverse functions to be θ, α, β respectively. Rearranging and taking tan of both sides

[itex]tan(\theta + \alpha) = tan(\pi - \beta) \\

tan(\theta + \alpha) = -tan(\beta)

[/itex]

After simplifying I get something like this

[itex]x\sqrt{(1-y^2)(1-z^2)}+y\sqrt{(1-x^2)(1-z^2)}+z\sqrt{(1-x^2)(1-y^2)} = xyz[/itex]

I know it's close but it is not yet the final result.