10 класс профильная 5cosα+6sinα / 3sinα-7cosα если tgα = 1/2 и еще 2sin³α + 3cos³α / 5sinα - cosα если tgα = -4

1) (5cosα+6sinα) / (3sinα-7cosα) = (числитель и знаменатель делим на cosα)=

= (5+6tgα) / (3tgα-7) = (5+6·(1/2)) / (3·(1/2)-7) = (5+3) / (1,5-7) = 8/(-5.5) = -80/55 = -16/11 = -1 5/11.

2) (2sin³α + 3cos³α) / (5sinα - cosα) = (cos³α(2tg³α + 3)) / (cosα(5tgα - 1)) =

= (cos²α(2tg³α + 3)) / (5tgα - 1) = (2tg³α + 3) / ((1/cos²α)(5tgα - 1)) =

= (2tg³α + 3) / ((1+tg²α)(5tgα - 1)) = (2(-4)³ + 3) / ((1+(-4)²)(5(-4) - 1)) =

= (-128 + 3) / ((1+16)(-20 - 1)) = -125/(-357) = 125/357