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

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

1. Take L.H.S sin2A+sin5A-sinA/cos2A+cos5A+cosA
2. Put sinC-sinD and cosC+cosD
3. On solving we get, sin2A+2cos3A.sin2A/cos2A+2cos3A.cos2A
4. Taking common sin2A from numenitor and cos2A from denominator.
5. Finally we get sin2A/cos2A
6. Hence we proved sin2A+sin5A-sinA/cos2A+cos5A+cosA=tan2A

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