Упростите выражение (3sin t+4cos t)^2+(4sin t-3 cos t)^2 (3sin t+4cos t)^2+(4sin t-3 cos t)^2

(3sin t+4cos t)^2 + (4sin t-3 cos t)^2 =
= 9sin^2 t + 24sin t * cos t + 16*cos^2 t + 16*sin^2 t - 24sin t * cos t + 9cos^2 t =

= 9sin^2 t + 16*cos^2 t + 16*sin^2 t + 9cos^2 t =

= 25sin^2 t + 25cos^2 t =

= 25 * (sin^2 t + cos^2 t) = 25 * 1 = 25