Prove that, for 0
sin^2 A+sin^2 A cos^2 A+sin^2 A cos^4 A+sin^2 A cos^6 A+...=1
sin^2 A+sin^2 A cos^2 A+sin^2 A cos^4 A+sin^2 A cos^6 A+...=1
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sin^2 A+sin^2 A cos^2 A+sin^2 A cos^4 A+sin^2 A cos^6 A+...
= sin^2A/(1-cos^2A)
= sin^2A/sin^2A
= 1
QED
= sin^2A/(1-cos^2A)
= sin^2A/sin^2A
= 1
QED
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sin^2 A+sin^2 A cos^2 A+sin^2 A cos^4 A+sin^2 A cos^6 A+..
= sin^2 A ( 1 + cos^2 A + cos^4 A + cos ^6 A +.....)
= sin^2 A (1 / ( 1- cos^2 A) = sin ^2 A ( 1/ sin^2 A ) = 1
= sin^2 A ( 1 + cos^2 A + cos^4 A + cos ^6 A +.....)
= sin^2 A (1 / ( 1- cos^2 A) = sin ^2 A ( 1/ sin^2 A ) = 1