Question

If number of value of A in [0,2pi] for expression sin²A=(x²+y²)/(2xy) for all x, y is element of 'R' - {0} is satisfied, is

Answer 1

dear student

$$\begin{gathered} {\sin }^{2}A=\frac{x^2+y^2}{2xy} \\ NowAM\ge GM \\ soforpositivenumbers{x}^{2}and{y}^2 \\ \frac{x^2+y^2}{2}\ge \sqrt{x^2{y}^2} \\ \frac{x^2+y^2}{2}\ge xy \\ \frac{x^2+y^2}{2xy}\ge 1 \\ Butsi{n}^{2}A=\frac{x^2+y^2}{2xy} \\ soleasvalueofsi{n}^{2}A=1 \\ \sin A=\pm 1 \\ intherangeof0to2\mathrm{\pi } \\ \mathrm{A}\mathrm{can}\mathrm{take}\mathrm{values}\mathrm{\pi }/2\mathrm{and}3\mathrm{\pi }/2 \\ \mathrm{so}\mathrm{number}\mathrm{of}\mathrm{values}\mathrm{of}\mathrm{A}=2 \end{gathered}$$

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