Question:
If sinθ + cosθ = 1, then the value of sin 2θ is ___________.
Solution:
Given $\sin \theta+\cos \theta=1$
By squaring both sides, we get
$(\sin \theta+\cos \theta)^{2}=(1)^{2}$
i. e. $\sin 2 \theta+\cos ^{2} \theta+2 \sin \theta \cos \theta=1$
i. e. $1+2 \sin \theta \cos \theta=1$
i.e. $2 \sin \theta \cos \theta=0$
i.e. $\sin 2 \theta=0$
Hence, value of $\sin 2 \theta$ is 0 .
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