CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions1 Mark
MCQ
If $\sin\theta+\cos\theta=1,$ then the value of $\sin2\theta$ is equal to:
A
$1$
B
$\frac{1}{2}$
✓
$0$
D
$-1$
✓
Answer
Correct option: C.
$0$
Given that, $\sin\theta+\cos\theta=1$
Squaring both sides, we get,
$\Rightarrow(\sin\theta+\cos\theta)^2=(1)^2$
$\Rightarrow\sin^2\theta+\cos^2\theta+2\sin\theta\cos\theta=1$
$\Rightarrow1+\sin2\theta=1$
$\Rightarrow\sin2\theta=1-1=0$
Hence, the correct option is $(c).$
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