Final answer to the problem
Step-by-step Solution
Specify the solving method
We can multiply the polynomials $\left(\csc\left(x\right)+\cot\left(x\right)\right)\left(1-\cos\left(x\right)\right)$ by using the FOIL method. The acronym F O I L stands for multiplying the terms in each bracket in the following order: First by First ($F\times F$), Outer by Outer ($O\times O$), Inner by Inner ($I\times I$), Last by Last ($L\times L$)
Learn how to solve problems step by step online.
$\begin{matrix}(F\times F)\:=\:(\csc\left(x\right))(-\cos\left(x\right))\\(O\times O)\:=\:(\csc\left(x\right))(1)\\(I\times I)\:=\:(\cot\left(x\right))(-\cos\left(x\right))\\(L\times L)\:=\:(\cot\left(x\right))(1)\end{matrix}$
Learn how to solve problems step by step online. Expand and simplify the trigonometric expression (csc(x)+cot(x))(1-cos(x)). We can multiply the polynomials \left(\csc\left(x\right)+\cot\left(x\right)\right)\left(1-\cos\left(x\right)\right) by using the FOIL method. The acronym F O I L stands for multiplying the terms in each bracket in the following order: First by First (F\times F), Outer by Outer (O\times O), Inner by Inner (I\times I), Last by Last (L\times L). Then, combine the four terms in a sum. Substitute the values of the products. Any expression multiplied by 1 is equal to itself.