Factor the algebraic expression below in terms of a single trigonometric function. sin 2x + sin x - 2

Answer:The factored form is (sin x +2)(sin x-1)Step-by-step explanation:We have been given the trigonometric function [tex]\sin^2 x +\sinx-2[/tex]We can factor this by AC method. In AC method we multiply the term a and c and then write the middle term b in such a way that the sum/difference is equal to the product 'ac'Using the method, we can write sinx as 2sinx -sinx[tex]\sin^2 x +2\sinx-\sin x-2[/tex]Now, we group the first two terms and the last two terms[tex](\sin^2 x +2\sinx)+(-\sin x-2)[/tex]Now, we take GCF from each group[tex]\sin x(\sin x +2)-1(\sin x+2)[/tex]Factor out (sinx+2)[tex](\sin x +2)(\sin x-1)[/tex]Therefore, the factored form is (sin x +2)(sin x-1)