[tex]{ \sin}^{2}40^{\circ} + \sin^{2} 50^{\circ} + { \sin}^{2}60^{\circ} = \\ \\ { \sin}^{2}(90^{\circ} - 50^{\circ}) + \sin^{2}50^{\circ} + { \sin}^{2}90^{\circ} - 30^{\circ} = \\ \\ { \cos}^{2}50^{\circ} + \sin^{2} 50^{\circ}+ { \cos}^{2}30^{\circ} = \\ \\ 1 + \cos^{2}30^{\circ} = \\ \\ 1 + (\frac{ \sqrt{3} }{2})^{2} =1 \frac{3}{4} \\ [/tex]
C
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[tex]{ \sin}^{2}40^{\circ} + \sin^{2} 50^{\circ} + { \sin}^{2}60^{\circ} = \\ \\ { \sin}^{2}(90^{\circ} - 50^{\circ}) + \sin^{2}50^{\circ} + { \sin}^{2}90^{\circ} - 30^{\circ} = \\ \\ { \cos}^{2}50^{\circ} + \sin^{2} 50^{\circ}+ { \cos}^{2}30^{\circ} = \\ \\ 1 + \cos^{2}30^{\circ} = \\ \\ 1 + (\frac{ \sqrt{3} }{2})^{2} =1 \frac{3}{4} \\ [/tex]
C