Could someone clarify these questions step-by-step?
Much appreciated! (sorry for my earlier thread!)
Solve within [0, 2pi):
cos2x + cosx = 0
cot²x - cos²x = cot²xcos²x
cot²x - cos²x = cot²xcos²x
cos^2x/sin^2x - cos^2x=cos^2x/sin^2x cos^2x
devide by cos^2x , => 1/sin^2x - 1 = cos^2x/sin^2x
=> 1-sin^2x = cos^2x
= cos^2x+sin^2x = 1 => 1=1 ... i cant understand the point from this simplification !!! check again your question , the first one will be similar
you need to look at the directions for these two equations again.
trig expressions are simplified ... trig equations are either identities to be verified or conditional equations to be solved.
the first equation is a conditional equation.
the second equation is an identity.
$\displaystyle cos(3x) = cos(2x+x) = cos(2x)cos(x)-sin(2x)sin(x)$
$\displaystyle
(2cos^2(x)-1)(cos(x))-2sin^2(x)cos(x) = 2cos^3(x)-cos(x)-2cos(x)+2cos^3(x)) $
$\displaystyle = 4cos^3(x)-3cos(x)$
$\displaystyle \therefore \: \: 4cos^3(x)-2cos(x)= 2cos(x)(2cos^2(x)-1)=0$