I took a guess on the question intended. If it's incorrect you'll need to ask it again, sorry.
#70^circ # and #20^circ# are complementary angles, which means they add to #90^circ.# The "co" in cosine means "complementary." It refers to the dual identities:
#cos(90^circ - theta) = sin theta #
#sin(90^circ - theta) = cos theta #
So
# cos 70^circ sin 20^circ = cos^2 70^circ = sin^2 20^\circ#
This angle isn't constructible so there's no nice form with integers combined via addition, subtraction, multiplication, division and square rooting.
# \cos ^2 70^circ # is indeed an algebraic number, meaning it's the root of a polynomial with integer coefficients. #70^circ# is a rational fraction of a circle, related to #1^circ#. Our number is a root #cos^2 theta# of an equation like #cos^2(179 theta) = cos^2(181 theta)#. Like the double angle formula, there's a 179th and 181st angle formula. Each side is a polynomial in #x=cos theta#. The degree is #362# because of the squaring.
