Question

Упростите выражение:
(ctg t - tg t) * 1/cos2t

Answer 1

$\displaystyle\bf\\\Big(Ctgt-tgt\Big)\cdot\frac{1}{Cos2 t} =\Big(\frac{Cost}{Sint} -\frac{Sint}{Cost}\Big)\cdot\frac{1}{Cos2t} =\\\\\\=\frac{Cos^{2} t-Sin^{2}t }{Sint\cdot Cost} \cdot\frac{1}{Cos2t} =\frac{Cos2t}{Sint\cdot Cost} \cdot\frac{1}{Cos2t}=\\\\\\=\frac{1}{Sint\cdot Cost} =\frac{2}{Sin2t}$