If sinθ + cosθ = 1, then the value of sin2θ

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If sinθ + cosθ = 1, then the value of sin2θ is equal to

1. 1
2. 1/2
3. 0
4. - 1

Correct Option: C

Here,
sinθ + cosθ = 1
Squaring on both sides, we get
(sinθ + cosθ)² = 1
sin²θ + cos²θ + 2sinθ × cosθ = 1
1 + 2sinθ cosθ = 1
2sinθ× cosθ = 0
And we know that,
sin2θ = 2sinθ cosθ
⇒ sin2θ = 0