Question 623872
{{{sin^4(x) + 2sin^2(x)cos^2(x) + cos^4(x) = 1}}}
I'm sure there are other ways to do this but probably the easiest is to recognize that the left side is a perfect square trinomial. It fits the pattern of:
{{{a^2+2ab+b^2 = (a+b)^2}}}
with the "a" being {{{sin^2(x)}}} and the "b" being {{{cos^2(x)}}}. Once we recognize this, the rest is easy. Factoring the left side according to the pattern we get"
{{{(sin^2(x) + cox^2(x))^2 = 1}}}
We should know well that {{{sin^2(x) + cox^2(x)}}} = 1, so this becomes:
{{{1^2 = 1}}}
which simplifies to:
{{{1 = 1}}}
And we're finished!!