If cos(x)cos(x-(Π/3))=1-(n/6), then the constraint of the value n that satisfies ?

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Answer 1 · 2018-08-12T12:49:48

#n in [ - 1/4, 7/4 ]#

#cos x cos ( x - pi/3 ) = cos x ( cosx cos (pi/3) + sin x sin (pi/3) )#

#= 1/2 ( cos^2x + sqrt3 sin x cos x )#

#= 1/2( 1/2(1 + cos 2x ) + 1/2sqrt 3 sin 2x )#

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

#= 1 -n/6#. So,

#cos ( 2x - pi/3 ) = 3/4 - n/6 in [ -1, 1 ]#

#rArr -n/6 in [ -1 - 3/4, 1 - 3/4 ] = [ - 7/4, 1/4 ]#

# n/6 in [ - 1/4, 7/4 ]#, and so,

#n in [ -3/2, 21/2 ]#