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[tex]\bf 12.10a)\ \ sin^4a\cdot cos^2a+sin^2a\cdot cos^4a=sin^2a\, cos^2a\, (\underbrace{\bf sin^2a+cos^2a}_{1})=\\\\=sin^2a\cdot cos^2a\\\\sin^2a\cdot cos^2a=sin^2a\cdot cos^2a\\\\b)\ \ \dfrac{sina+tga}{1+cosa}=\dfrac{sina+\dfrac{sina}{cosa}}{1+cosa}=\dfrac{sina\cdot cosa+sina}{cosa\, (1+cosa)}=\dfrac{sina\cdot (cosa+1)}{cosa\, (1+cosa)}=\\\\\\=\dfrac{sina}{cosa}=tga\\\\\\tga=tga[/tex]    

Объяснение:

1.

sin⁴α•cos²α+sin²α•cos⁴α=

=sin²α•cos²α•(sin²α+cos²α)=

=sin²α•cos²α•1=sin²α•cos²α

sin²α•cos²α=sin²α•cos²α - верно

2.

sinα

sinα+tgα sinα + ———

cosα

————— = ————————— =

1+cosα 1+cosα

sinα•cosα+sinα

——————————

cosα

= ——————————— =

1+cosα

sinα•cosα+sinα sinα(cosα+1)

= ————————— = ———————— =

cosα(1+cosα) cos(1+cosα)

sinα

= ——— = tgα

cosα

tgα=tgα -верно