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Simplify #cos(4theta)-4cos(2theta)+3#?

1 Answer

Nov 30, 2017

#2(cos(x)-1)^2#

Explanation:

I suppose you meant this,

#cos(4theta)-4cos(2theta)+3#

Let #2theta# be #x#, and we get this,

#cos(2x)-4cos(x)+3#

Using double angle formulae,

#cos(2x)-4cos(x)+3#
#=2cos^2(x)-1-4cos(x)+3#
#=2cos^2(x)-4cos(x)+2#
#=2(cos^2(x)-2cos(x)+1)#
#=2(cos(x)-1)^2#

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