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Question
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Solution
LHS = sin2 10° + sin2 20° + sin2 70° + sin2 80°
= sin2 10° + sin2 (90° – 10°) + sin2 20° + sin2(90° – 20°)
= sin2 10° + (cos 10°)2 + sin2 20° + (cos 20°)2
= (sin2 10+ cos2 10) + sin2 20° + cos2 20°
= 1 + 1
= 2
= R.H.S
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