Calculate the length AC by using[br][list][*]cosine rule[/*][*]pythagoras[/*][/list][br]What can you conclude about [math]\cos\left(\alpha+\beta\right)[/math]?[br][br]Calculate the area of the triangle OAB by using[br][list][*][math]\frac{1}{2}ab\sin\left(C\right)[/math][br][/*][*][math]\frac{1}{2}base\times height[/math] twice[/*][/list][left]BIG HINT: [br]The line AC crosses the x axis at [math]\cos\left(\alpha\right)+\frac{\sin\left(\alpha\right)}{\sin\left(\alpha\right)+\sin\left(\beta\right)}\left(\cos\left(\beta\right)-\cos\left(\alpha\right)\right)[/math][br]Can you see why?[/left]What can you conclude about [math]\sin\left(\alpha+\beta\right)[/math]?