Prove that sin2A+sin5A-sinA/cos2A+cos5A+cosA=tan2A

Steps to prove sin2A+sin5A-sinA/cos2A+cos5A+cosA=tan2A

Take L.H.S sin2A+sin5A-sinA/cos2A+cos5A+cosA

= sin2A+sin5A-sinA/cos2A+cos5A+cosA

= sin2A+{2cos(5A+A)/2 . sin(5A-A)/2} / cos2A+{2cos(5A+A)/2 . cos(5A-A) 

[ sinC-sinD=2.cos(C+D)/2.sin(C-D)/2]
[cosC+cosD=2.cos(C+D)/2.cos(C-D)/2]

=  sin2A+2cos3A.sin2A/cos2A+2cos3A.cos2A

= sin2A(1+2cos3A)/cos2A(1+2cos3A)

= sin2A/cos2A

= tan2A

= R.H.S

Detail Information:

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