I'm sorry, but two more questions please:)
sin(x) - sin(x) * cos^2(x)
sin^4(x) - cos^4(x) divided by sin^2(x) - cos^2(x)
+129847 sin(x) - sin(x) * cos^2(x) =
sin x - sin x * ( 1 - sin^2 x) =
sinx - sin x + sin^3 x =
sin^3 x
sin^4(x) - cos^4(x) divided by sin^2(x) - cos^2(x)
Factor sin^4 x - cos^4x as
[sin^2 x + cos ^2 x] [ sin^2 x - cos^2 x ] / [sin^2 x - cos^2 x ] =
sin^2 x + cos^2 x =
1
+118667 sin(x) - sin(x) * cos^2(x)
\(sin(x) - sin(x) * cos^2(x)\\ =sin(x) (1- cos^2(x))\\ =sin(x) sin^2(x)\\ =sin^3(x)\\ \)
sin^4(x) - cos^4(x) divided by sin^2(x) - cos^2(x)
\(\frac{sin^4(x) - cos^4(x) }{sin^2(x) - cos^2(x)}\\ =\frac{(sin^2(x) - cos^2(x))(sin^2(x) + cos^2(x)) }{sin^2(x) - cos^2(x)}\\ =\frac{sin^2(x) - cos^2(x)}{sin^2(x) - cos^2(x)}\\~\\ =1 \qquad where \;\;\; x\ne \frac{\pi+2n\pi}{4} \;\;\;n\in Z\)
