$(cos A + sin)^{2} - (cos A - sin A)^{2}$ Is equal to

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2 sin 2 A

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Solution

The correct option is D $2 sin 2 A$
As we know that $(a + b)^{2} - (a - b)^{2} = 4 a b$
Similarly,
$(c o s A + s i n A)^{2} - (c o s A - s i n A)^{2} = 4 c o s A s i n A$
and $s i n 2 A = 2 c o s A . s i n A$
$∴ (c o s A + s i n A)^{2} - (c o s A - s i n A)^{2} = 2 s i n 2 A$

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