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8. Introduction to Trigonometry
medium
$(\sin \theta+\cos \theta)^{2}+(\sin \theta-\cos \theta)^{2}=\ldots \ldots \ldots \ldots$
A
$4 \sin \theta \cos \theta$
B
$2$
C
$1$
D
$0$
Solution
$(\sin \theta+\cos \theta)^{2}+(\sin \theta-\cos \theta)^{2}$
$=\left(\sin ^{2} \theta+2 \sin \theta \cos \theta+\cos ^{2} \theta\right)+\left(\sin ^{2} \theta-2 \sin \theta \cos \theta+\cos ^{2} \theta\right)$
$=2 \sin ^{2} \theta+2 \cos ^{2} \theta$
$=2\left(\sin ^{2} \theta+\cos ^{2} \theta\right)=2(1)=2$
Standard 10
Mathematics
