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We can multiply the polynomials $\left(\sin\left(x\right)+\cos\left(x+1\right)\right)\left(\sin\left(x\right)+\cos\left(x-1\right)\right)$ 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 simplify trigonometric expressions problems step by step online.
$\begin{matrix}(F\times F)\:=\:(\sin\left(x\right))(\sin\left(x\right))\\(O\times O)\:=\:(\sin\left(x\right))(\cos\left(x-1\right))\\(I\times I)\:=\:(\cos\left(x+1\right))(\sin\left(x\right))\\(L\times L)\:=\:(\cos\left(x+1\right))(\cos\left(x-1\right))\end{matrix}$
Learn how to solve simplify trigonometric expressions problems step by step online. Expand and simplify the trigonometric expression (sin(x)+cos(x+1))(sin(x)+cos(x-1)). We can multiply the polynomials \left(\sin\left(x\right)+\cos\left(x+1\right)\right)\left(\sin\left(x\right)+\cos\left(x-1\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. When multiplying two powers that have the same base (\sin\left(x\right)), you can add the exponents.