Question

Упростите выражение:
1)1-sin^2a=
2)1+sin^2a+cos^2a=
3)(1-cosa)(1+cosa)=
4)sina-sina*cos^2a=sina*( )=
5)sin^4a+2sin^2a*cos^2a+cos^4a=
6)tg^2a-sin^2a*tg^2a=
7)cos^2a+cos^2a*tg^2a=
8)tg&2a*(2cos^2a+sin^2a-1)=

Answer 1

1) 1-sin^2a= cos^2a
2) 1+sin^2a+cos^2a = 2
3) (1-cosa) (1+cosa) = 1-cos^2a = sin^2a
4) sina - sina*cos^2a= sina(1-cos^2a) = sin^3a
5) sin^4 + 2sin^2a*cos^2a + cos^4a = (sin^2a+cos^2a) ^2= 1
6) tg^2a-sin^2a*tg^2a = tg^2a (1-sin^2a) = sin^2a/cos^2a * cos^2a = sin^2a
7) cos^2a + cos^2a*tg^2a = cos^2a + cos^2a*sin^2a/cos^2a = cos^2a + sin^2a = 1
8) tg^2a ( 2cos^2a + sin^2a- 1) = tg^2a*(2cos^2a-cos^2a) = sin^2a/cos^2a * cos^2a = sin^2a