[tex]\sin x + \cos x = \dfrac{5}{4} \Rightarrow (\sin x + \cos x)^2 = \left(\dfrac{5}{4}\right)^2
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\sin^2 x + \cos^2 x +2 \sin x \cos x = \dfrac{25}{16}
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1 +2 \sin x \cos x = \dfrac{25}{16} \Rightarrow 2 \sin x \cos x = \dfrac{25}{16} -1
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\sin2x=\dfrac{9}{16}[/tex]