Упростить уравнение:

а) (tga+ctga) * (1+cosa) * (1-cosa)

б) cos^3a+sin^3a/sina+cos^3a-sin^3a/cosa

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