For a geometric series question:
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For a geometric series question:

[From: ] [author: ] [Date: 11-12-20] [Hit: ]
=1-sin^2 A+sin^2 A cos^2 A+sin^2 A cos^4 A+sin^2 A cos^6 A+...QED-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 +.......
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

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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

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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
1
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