- #1

utkarshakash

Gold Member

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## Homework Statement

If [itex]cos^{-1}\frac{x}{a}+cos^{-1}\frac{y}{b} = \alpha[/itex] then show that [itex]\frac{x^2}{a^2}-\frac{2xy}{ab}cos \alpha + \frac{y^2}{b^2} = sin^2 \alpha[/itex]

## Homework Equations

## The Attempt at a Solution

I assume inverse functions to be θ and β respectively. So in the second equation for LHS I can convert it like this

[itex] cos^2\theta + cos^2\beta - 2cos \alpha cos\theta cos\beta [/itex]

Similarly for RHS

[itex] sin^2 \alpha = sin^2(\theta + \beta)[/itex]