Provev that:cos2x/cosx-sinx=cosx+sinx?

1 Answer
May 20, 2018

#"see explanation"#

Explanation:

#"using the "color(blue)"trigonometric identity"#

#•color(white)(x)cos2x=cos^2x-sin^2x#

#"consider the left side"#

#(cos^2x-sin^2x)/(cosx-sinx)#

#cos^2x-sin^2x" is a "color(blue)"difference of squares"#

#=(cancel((cosx-sinx))(cosx+sinx))/cancel(cosx-sinx)#

#=cosx+sinx=" right side "rArr"verified"#