Question

If sinθ + cosθ = 1, then the value of sin 2θ is ___________.

Answer 1

$$\begin{gathered} \mathrm{Given}\sin \theta +\cos \theta =1 \\ \mathrm{By}\mathrm{squaring}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ {\left(\sin \theta +\cos \theta \right)}^2={\left(1\right)}^2 \\ \mathrm{i}.\mathrm{e}.\sin 2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =1 \\ \mathrm{i}.\mathrm{e}.1+2\sin \theta \cos \theta =1 \\ \mathrm{i}.\mathrm{e}.2\sin \theta \cos \theta =0 \\ \mathrm{i}.\mathrm{e}.\sin 2\theta =0 \\ \mathrm{Hence},\mathrm{value}\mathrm{of}\sin 2\theta \mathrm{is}0. \end{gathered}$$