Question

(sin^6+cos^6)/0,125
если sina-cosa=0,5

Answer 1

sina-cosa=0.5
(sina-cosa)^2=0.25
1-2sinacosa=0.25
-2sinacosa=-0.75
sinacosa=0.375

( (sin^2a)^3+(cos^2a)^3  )/0.125=( (sin^2a+cos^2a)(sin^4-sin^2a*cos^2a+cos^4a)  )/0.125
=1*(sin^4-sin^2a*cos^2a+cos^4a)  )/0.125=
(sin^4a-sin^2a*cos^2a+cos^4a-sin^2a*cos^2a+sin^2a*cos^2a)  )/0.125=
(  (si^2a-cos^2a)^2+sin^2a*cos^2a)/0.125=
(  (sina-cosa)^2*(sina+cosa)^2+sin^2acos^2a)/0.125=
(0.25*(sin^2a+2sina*cosa+cos^2a)+sin^2acos^2a)/0.125=
(0.25(1+2sinacosa)+sin^2acos^2a)/0.125=
(0.25(1+2*0.375)+0.375^2)/0.125=
(0.25*1.75+0140625)/0.125=
(0.4375+0140625)/0.125=0.578125/0.125=4.625