Question #32396

1 Answer
May 18, 2016

The equation as given is invalid.
See below for a proof that assumes the exponents were omitted and the equation should be:
#sin(x)-sin(x)cos^2(x)=sin^3(x)#

Explanation:

#sin(x)-sin(x)cos^2(x)#

factoring:
#color(white)("XXX")=sin(x)*(1-cos^2(x))#

Since #sin^2(x)+cos^2(x)=1#
#color(white)("XXX")#we know this as a standard identity
#color(white)("XXX")#or we could develop it easily from Pythagorean theorem and definition of #sin# and #cos#

#sin(x)*(color(red)(1-cos^2(x)))#
#color(white)("XXX")=sin(x)*color(red)(sin^2(x))#

#color(white)("XXX")=sin^3(x)#