Question

Упростить уравнение:
а) (tga+ctga)*(1+cosa)*(1-cosa)
б) cos^3a+sin^3a/sina+cos^3a-sin^3a/cosa

Answer 1

Упростить выражения:

а) (tga+ctga)*(1+cosa)*(1-cosa)=(sina/cosa+cosa/sina)(1-cos²a)=
=[(sin²a+cos²a)/(cosa·sina)](1-cos²a)=[1/(cosa·sina)](sin²a)=sina/cosa=tga
б) (cos^4(a)+sin^3(a)·cos(a)+cos^3(a)·sin(a) -sin^4(a))/(sin(a)·cos(a))=
=[(cos^4(a)-sin^4(a)+sin(a)·cos(a)·(sin^2(a)+cos^2(a))] /(sin(a)·cos(a))=
=[(cos^2(a)-sin^2(a))(cos^2(a)+sin^2(a))+sin(a)·cos(a)·1)] /(sin(a)·cos(a))==[(cos^2(a)-sin^2(a))·1)+sin(a)·cos(a)·1)] /(sin(a)·cos(a))=
=cos(2a)/[(1/2)sin(2a)]+1=2·ctg(2a)+1