Решение:
sin^2(7π/2 - a) = sin^2(π/2 - a) = sin^2(π/2)cos^2(a) - sin(π/2)sin(a)cos(a) = cos^2(a)
sin^2(6π + a) = sin^2(a) = cos^2(a)
Таким образом, sin^2(7π/2 - a) + sin^2(6π + a) = cos^2(a) + cos^2(a) = 2cos^2(a)
Ответ: 2cos^2(a)
Решение:
sin^2(7π/2 - a) = sin^2(π/2 - a) = sin^2(π/2)cos^2(a) - sin(π/2)sin(a)cos(a) = cos^2(a)
sin^2(6π + a) = sin^2(a) = cos^2(a)
Таким образом, sin^2(7π/2 - a) + sin^2(6π + a) = cos^2(a) + cos^2(a) = 2cos^2(a)
Ответ: 2cos^2(a)