Question

Упростите выражение с тригонометрическими функциями

Answer 1

Ответ:

$\displaystyle \frac{sin4a}{1+cos4a}\cdot \frac{cos2a}{1+cos2a}=\frac{2\, sin2a\cdot cos2a}{2cos^22a}\cdot \frac{cos2a}{2\, cos^2a}=\frac{sin2a}{2\, cos^2a}=\\\\\\=\frac{2\, sina\cdot cosa}{2\, cos^2a}=\frac{sina}{cosa}=\, tga$

Answer 2

$\dfrac{Sin4\alpha }{1+Cos4\alpha } \cdot\dfrac{Cos2\alpha }{1+Cos2\alpha } =\dfrac{2Sin2\alpha Cos2\alpha}{2Cos^{2}2\alpha}\cdot\dfrac{Cos2\alpha }{2Cos^{2}\alpha} =\dfrac{Sin2\alpha\cdot Cos2\alpha}{Cos2\alpha\cdot 2Cos^{2}\alpha } =\\\\=\dfrac{Sin2\alpha }{2Cos^{2}\alpha}=\dfrac{2Sin\alpha Cos\alpha}{2Cos^{2}\alpha}=\dfrac{Sin\alpha }{Cos\alpha }=\boxed{tg\alpha}$