How to verify identity of sin 4x tan 2x = 1 - cos 4x ?

1 Answer
May 10, 2018

The answer
#sin4x*tan2x =1-cos4x#

#L.H.S=sin4x*tan4x=sin4x*[(sin2x)/(cos2x)]#

#=sin2x*[(sin2(2x))/(cos2x)]=sin2x*[(2*sin2x*cos2x)/(cos2x)]#

#=sin2x*[2*sin2x]=2sin^2(2x)#

#2*[1/2(1-cos4x)]=1-cos4x=R.H.S#

Explanation:

your identify

#sin4x*tan2x =1-cos4x#

#L.H.S=sin4x*tan4x=sin4x*[(sin2x)/(cos2x)]#

#=sin2x*[(sin2(2x))/(cos2x)]=sin2x*[(2*sin2x*cos2x)/(cos2x)]#

#=sin2x*[2*sin2x]=2sin^2(2x)#

#2*[1/2(1-cos4x)]=1-cos4x=R.H.S#

Note that

#sin2x=2*sinx*cosx#

#cos2x=cos^2x-sin^2x#

#sin^2x=1/2*[1-cos2x]#

#cos^2x=1/2*[1+cos2x]#