verify: $(1 - c o s^{2} y + s i n^{2} y)^{2} + 4 s i n^{2} y c o s^{2} y = 4 s i n^{2} y$

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Solution

$L H S = ((1 - c o s^{2} y) + s i n^{2} y)^{2} + 4 s i n^{2} y c o s^{2} y$
$= (s i n^{2} y + s i n^{2} y)^{2} + 4 s i n^{2} y c o s^{2} y$
$= (2 s i n^{2} y)^{2} + 4 s i n^{2} y c o s^{2} y$
$= 4 s i n^{4} y + 4 s i n^{2} y c o s^{2} y$
$= 4 s i n^{2} y (s i n^{2} y + c o s^{2} y)$
$= 4 s i n^{2} y * 1$
$= 4 s i n^{2} y$
$= R H S$

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