NARRATOR: Exercise 7.
Prove that 1 divided by sec theta plus tan theta
is equal to cos theta divided by 1 plus sin theta.
We begin with the left-hand side,
1 divided by sec theta plus tan theta,
and write this out as a division
so that we can express sec theta and tan theta as fractions.
So we have 1 divided by 1 over cos theta plus sin theta over cos theta.
So that is 1 divided by 1 plus sin theta all divided by cos theta,
which is equivalent to
1 multiplied by cos theta divided by 1 plus sin theta,
which equals cos theta
divided by 1 plus sin theta,
which is equal to
the right-hand side,
and so we have proven that
1 divided by sec theta plus tan theta
equals cos theta
divided by 1 plus sin theta
as was required.