Question

Даю 30 баллов. Спасибо заранее.

Answer 1

Ответ:

Объяснение:

1) $\dfrac{sin^2\alpha -cos^2\alpha +cos^4 \alpha }{cos^2\alpha -sin^2\alpha +sin^4 \alpha } = \dfrac{sin^2\alpha -cos^2\alpha (1-cos^2 \alpha) }{cos^2\alpha -sin^2\alpha (1-sin^2 \alpha) } =$

$= \dfrac{sin^2\alpha -cos^2\alpha sin^2 \alpha }{cos^2\alpha -sin^2\alpha cos^2 \alpha } = \dfrac{sin^2\alpha(1 -cos^2\alpha) }{cos^2\alpha(1 -sin^2\alpha) }= \\\\\\= \dfrac{sin^2\alpha\cdot sin^2 \alpha}{cos^2\alpha \cdot cos^2 \alpha } = tg^4 \alpha$

2) $\dfrac{3sin^2\alpha+cos^4\alpha}{1+sin^2\alpha +sin^4\alpha } = \dfrac{3sin^2\alpha+(1-sin^2\alpha)^2}{1+sin^2\alpha +sin^4\alpha }=$

$= \dfrac{3sin^2\alpha+1-2sin^2\alpha+sin^4 \alpha }{1+sin^2\alpha +sin^4\alpha }=\dfrac{1+sin^2\alpha +sin^4\alpha }{1+sin^2\alpha +sin^4\alpha }= 1$