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(sin6A+sin2A+2sin4A)/(sin7A+sin3A+2sin5A...

`(sin6A+sin2A+2sin4A)/(sin7A+sin3A+2sin5A)=(sin4A)/(sin5A)`

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(sin A+2sin3A+sin5A)/(sin3A+2sin5A+sin7A)=(sin3A)/(sin5A)

prove that : (sinA+2sin3A+sin5A)/(sin3A+2sin5A+sin7A)=(sin3A)/(sin5A)

sin A sin2A + sin3A sin6A-sin4A sin5A = 0

sin A+sin3A+sin5A+sin7A=

sin A+ sin 3A+ sin 5A + sin 7A=

(sin A sin2A + sin3A sin6A + sin4A sin13A) / (sin A cos2A + sin3A cos6A + sin4A cos13A) = tan9A

(cos3A-cos A)/(sin3A-sin A)+(cos2A-cos4A)/(sin4A-sin2A)=(sin A)/(cos2A cos3A)

(cos2A cos3A-cos2A cos7A+cos A cos10A)/(sin4A sin3A-sin2A sin5A+sin4A sin7A)=cot6A cot5A

(cos2A cos3A-cos2A cos7A+cos A cos10A)/(sin4A sin3A-sin2A sin5A+sin4A sin7A)=cot6A*cot5A

Prove that: (cos2A\ cos3A-cos2Acos7A+cos10 A cos A)/(sin4A\ sin3A-sin2A sin5A+sin4Asin7A )=cot6A\ cot5A