Question

найти sin^4a+cos^4a, если cosa+sina=1/3​

Answer 1

Ответ:

$C) 49/81$

Объяснение:

$sina+cosa=1/3\(sina+cosa)^2=(1/3)^2\sin^2+cos^2a+2sina*cosa=1/9\1+2sina*cosa=1/9\2sina*cosa=-8/9\sina*cosa=-8/18\sina*cosa=-4/9\sin^2a*cos^2=(-4/9)^2\sin^2a*cos^2a=16/81\\sin^4a+cos^4a=(sin^2a)^2+(cos^2)^2+2sin^2a*cos^2a-2sin^2a*cos^2a=\=(sin^2a+cos^2a)-2sin^2a*cos^2a=1-2sin^2a*cos^2a=\=1-2*16/81=1-32/81=49/81$