How to verify identity of sin 4x tan 2x = 1 - cos 4x ? Trigonometry 1 Answer James 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]# Answer link Related questions How do I determine the molecular shape of a molecule? What is the lewis structure for co2? What is the lewis structure for hcn? How is vsepr used to classify molecules? What are the units used for the ideal gas law? How does Charle's law relate to breathing? What is the ideal gas law constant? How do you calculate the ideal gas law constant? How do you find density in the ideal gas law? Does ideal gas law apply to liquids? Impact of this question 800 views around the world You can reuse this answer Creative Commons License