Question

Prove that: (sin to the power 4 theta+ cos to the power 4 theta) divided by 1-2 sin square theta cos square theta = 1

Answer 1

as you know
$a^4+b^4 = (a^2+b^2)^2-2a^2b^2$
and
$sin^2(x) + cos^2(x) = 1$
So
[tex] \frac{sin^4(x) + cos^4(x)}{1-2sin^2(x)cos^2(x) } = \frac{(sin^2(x)+cos^2(x))^2-2sin^2(x)cos^2(x) }{1-2sin^2(x)cos^2(x)} = \\ \frac{1-2sin^2(x)cos^2(x)}{1-2sin^2(x)cos^2(x)} = 1[/tex]