If sin θ + cos θ = 1,


If sin θ + cos θ = 1, then the value of sin 2θ is equal to

(a) 1

(b) $\frac{1}{2}$

(c) 0

(d) –1


Given, $\sin \theta+\cos \theta=1$

By squaring both sides,

we get, $(\sin \theta+\cos \theta)^{2}=(1)^{2}=1$

i.e. $\sin ^{2} \theta+\cos ^{2} \theta+2 \sin \theta \cos \theta=1$

i. e. $1+2 \sin \theta \cos \theta=1$

Since $\sin ^{2} \theta+\cos ^{2} \theta=1$      (using identity)

1.e. $2 \sin \theta \cos \theta=0$

$\Rightarrow \sin 2 \theta=0$

Hence, the correct answer is option C.

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