Question

2cos²asin²a+cos⁴a+sin⁴a

Answer 1

$2cos^2\alpha \cdot \:sin^2\alpha +cos^4\alpha +sin^4\alpha =\\\\= (\sin ^4 (\alpha )+\sin ^2 (\alpha )\cos ^2 (\alpha ) )+ (\sin ^2 (\alpha )\cos ^2 (\alpha )+\cos ^4 (\alpha ) )=\\\\=\sin ^2 (\alpha ) (\sin ^2 (\alpha )+\cos ^2 (\alpha ) )+\cos ^2 (\alpha ) (\sin ^2 (\alpha )+\cos ^2 (\alpha ) )=\\\\= (\sin ^2 (\alpha )+\cos ^2 (\alpha ) ) (\sin ^2 (\alpha )+\cos ^2 (\alpha ) )=\\\\= (\sin ^2 (\alpha )+\cos ^2 (\alpha ) )^2\\\\=1^2=1$