How do you prove that #cos2x+cosx=(cosx+1)(2cosx-1)#?
2 Answers
May 26, 2018
May 26, 2018
Explanation:
#"using the "color(blue)"trigonometric identity"#
#•color(white)(x)cos2x=2cos^2x-1#
#"consider the left side"#
#2cos^2x-1+cosx#
#=2cos^2x+cosx-1#
#"this is a quadratic in cos"#
#"the factors of the product "2xx-1=-2#
#"which sum to + 1 are + 2 and - 1"#
#"split the middle term using these factors"#
#2cos^2x+2cosx-cosx-1larrcolor(blue)"factor by grouping"#
#=2cosx(cosx+1)-1(cosx+1)#
#=(cosx+1)(2cosx-1)#
#="right side"rArr"verified"#