Так, сначала работем с числителем: 1-sin^2альфа+cos^2альфа*sinальфа)=(sin^2+cos^2-sin^2альфа+cos^2альфа*sinальфа)
Решение
sin^6(a)+cos⁶(a) = (sin²a)³ + (cos²a)³ =
(sin²a + cos²a)*(sin⁴a - sin²acos²a + cos⁴a) =
= [(sin⁴a + 2sin²acos²a + cos⁴a) - 3sin²acos²a] =
(sin²a + cos²a)² - 3sin<span>²acos²a =
= 1 - </span>3sin²acos²a = 1 - (3/4)*(2sinacosa)*(<span>2sinacosa) =
= 1 - (3/4)*(sin</span>²2a) = 1 - [(1 - cos4a)/2] =
= 1 - 3/8 + (3/8)*cos4a = 5/8 + <span> (3/8)*cos4a = (1/8)*(3cos4a + 5)</span>
A^2 * n^2 - 14^2 = (an)^2 - 196
= 1 - (sinα·cosα·cosα)/sinα+cos²α=1- cos²α+cos²α = 1