Question

А) sin2 а - cos2 а + 1; д) cos2 а + 2 sin2 а - 1; б) 1 + cos2 а - sin2 а; е) 2 cos2 а + sin2 а - 1; в) 1 - sin2 а - cos2 а; ж) 1 - 2 sin2 а - cos2 а; г) sin2 а - 1 + cos2 а; з) 1 - sin2 а - 2 cos2 ос. Преобразуйте выражение

Answer 1

I hope this helps you

Answer 2

выражение можно преобразовать следующим образом:

а) sin^2(a) - cos^2(a) + 1 = sin^2(a) + (1 - cos^2(a)) = sin^2(a) + sin^2(a) = 2sin^2(a)

д) cos^2(a) + 2sin^2(a) - 1 = cos^2(a) + (2sin^2(a) - 1) = cos^2(a) + cos^2(a) = 2cos^2(a)

б) 1 + cos^2(a) - sin^2(a) = 1 + (cos^2(a) - sin^2(a)) = 1 + cos(2a)

е) 2cos^2(a) + sin^2(a) - 1 = 2cos^2(a) + (sin^2(a) - 1) = 2cos^2(a) - cos^2(a) = cos^2(a)

в) 1 - sin^2(a) - cos^2(a) = 1 - (sin^2(a) + cos^2(a)) = 1 - 1 = 0

ж) 1 - 2sin^2(a) - cos^2(a) = 1 - (2sin^2(a) + cos^2(a)) = 1 - (1 - cos^2(a)) = cos^2(a)

г) sin^2(a) - 1 + cos^2(a) = (sin^2(a) + cos^2(a)) - 1 = 1 - 1 = 0

з) 1 - sin^2(a) - 2cos^2(a) = 1 - (sin^2(a) + 2cos^2(a)) = 1 - (1 - sin^2(a)) = sin^2(a)