Simplify the expression $\tan\left(\frac{x}{2}+45circ\right)^2=\frac{1+\sin\left(x\right)}{1+\sin\left(x\right)}$

 Main Topic: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.