Question

Упростите выражения:а) 1-sin²α б) 1-cos²α в) sin²α-1 г) cos²αа) (1+sin α)(1-sin α) б)(cos α-1)(1+cos α)в)cos²α-sin²α+1 г) 1+sin²α-cos²αа) 1-sin²α-cos²αб) sin^4 α-cos^4 αв) sin^4 α-cos^4 α-sin² α+cos²αг) (sin α+cos α)²+ (sin α-cos α)²

Answer 1

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

б)1-c0s^2a=sin^2a

b)sin^2a-1=sin^a-cos^2a-sin^2a=-cos^2a

г)cos^2a=1-sin^2a

 

a)(1+sina)(1-sina)=1-sin^2a

б)(cosa-1)(1+cosa)=cos^2a-1

b)cos^2a-sin^2a+1=cos^2a-sin^2a+cos^2a+sin^2a=2cos^2a

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

 

a)1-sin^2a-cos^2a=cos^2a-cos^2a=0

sin^4a-cos^4a=(sin^2a-cos^2a)(sin^2a+cos^2a)=sin^2a-cos^2a=-(cos^2a-sin^2a)=-cos2a

b)sin^4a-cos^4a-(cos^2a-sin^2a)=-cos2a-cos2a=-2cos2a

г)(sina+cosa)^2+(sina-cosa)^2=1+2sinacosa+1-2sinacosa=2