Question

Упростите выражение
$( \frac{1}{sin {}^{2}a } + \frac{1}{cos {}^{2}a } ) \times sin {}^{2} 2a$
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Answer 1

$\displaystyle\bf\\\Big(\frac{1}{Sin^{2}\alpha} +\frac{1}{Cos^{2}\alpha} \Big)\cdot Sin^{2}2\alpha =\frac{Cos^{2}\alpha +Sin^{2} \alpha}{Sin^{2}\alpha \cdot Cos^{2}\alpha} \cdot Sin^{2} 2\alpha =\\\\\\=\frac{1}{\frac{1}{4} \cdot 4\cdot Sin^{2} \alpha \cdot Cos^{2}\alpha} \cdot Sin^{2}2\alpha =\frac{4Sin^{2} 2\alpha }{Sin^{2} 2\alpha } =4$