Question

sin x +cos x= 5/4. calculati sin 2x.

Answer 1

$(sinx+cosx)^{2} = sin^{2}x+2sinxcosx+cos^2x \\ (\frac{5}{4} )^{2} = 1+sin2x \Rightarrow sin2x= \frac{25}{16} -1 \Rightarrow sin2x = \frac{25-16}{16} \Rightarrow \\ \Rightarrow sin2x = \frac{9}{16}$