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(1-\sin A+\cos A)^{2}$ is equal to
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Verified Answer
The correct answer is:
$2(1-\sin A)(1+\cos A)$
$(1-\sin A+\cos A)^{2}$
$=1+\sin ^{2} A+\cos ^{2} A-2 \sin A$
$\quad-2 \sin A \cdot \cos A+2 \cos A$
$=2-2 \sin A-2 \sin A \cos A+2 \cos A$
$=2(1-\sin A)+2 \cos A(1-\sin A)$
$=2(1+\cos A)(1-\sin A)$
$\therefore \quad$ Option (b) is correct.
$=1+\sin ^{2} A+\cos ^{2} A-2 \sin A$
$\quad-2 \sin A \cdot \cos A+2 \cos A$
$=2-2 \sin A-2 \sin A \cos A+2 \cos A$
$=2(1-\sin A)+2 \cos A(1-\sin A)$
$=2(1+\cos A)(1-\sin A)$
$\therefore \quad$ Option (b) is correct.
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