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Show that sin^2(π/18) + sin^2(π/9) + sin(7π/18) + sin^2(4π/9) = 2.

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Show that sin2(π/18) + sin2(π/9) + sin(7π/18) + sin2(4π/9) = 2.

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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 = RHS

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