( 1 - cos A ) ( 1 + sec A ) = tan A sin A
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1(1+sec A)-cos A(1+sec A)
1+sec A-cos A -1
sec A-cos A
1/cos A-cos A
1-cos^2 A/cos A
Sin^2 A/cos A
Sin A*Sin A/cos A
tan A sin A
Hence proved.
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