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Question
If sinθ + cosθ = 1, then the value of sin2θ is equal to ______.
Options
1
`1/2`
0
–1
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Solution
If sinθ + cosθ = 1, then the value of sin2θ is equal to 0.
Explanation:
Given that: sinθ + cosθ = 1
⇒ (sinθ + cosθ)2 = (1)2
⇒ sin2θ + cos2θ + 2sinθ cosθ = 1
⇒ 1 + sin2θ = 1
⇒ sin2θ = 1 – 1 = 0
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