Question

Simplify $sin x^{2} (x)cos x^{2} (x)-cos x^{2} (x)$
the x is the theta (the zero with the dash/mark through it)
much help would be appreciated for this problem

Answer 1

$sin^2(x)cos^2(x)-cos^2(x)\\\\=sin^2(x)\cdot cos^2(x)-1\cdot cos^2(x)\\\\=cos^2(x)\cdot(sin^2(x)-1)\\\\=cos^2(x)\cdot[-(1-sin^2(x)]^{(*)}\\\\=cos^2(x)\cdot[-cos^2(x)]^{(*)}\\\\\boxed{=-cos^4(x)}\\------------------\\(*)\ used:\\\\sin^2(x)+cos^2(x)=1\to cos^2(x)=1-sin^2(x)$

Answer 2

sinx²(x)cosx²(x) - cosx²(x)
sinx³cosx³ - cosx³
(0.01570731731x³)(0.9998766325x³) - 0.998766325x³
0.01570537954x³ - 0.998766325x³
-0.9841712529x³