Use $C$ to denote $\cos x$, and express
$1+\tan^2(x) =$ in terms of $C$.
Similarly, express
$(1-\sin x)(1+\sin x) =$ in terms of $C$.
Hint: For the first part use the definition of the tangent function. For the second part use the third binomial formula: $$(a+b)(a-b) = a^2-b^2.$$