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"