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Prove that: `sin^2pi/(18)+sin^2pi/9+sin^2(7pi)/(18)+sin^2(4pi)/9=2`

Answer» `L.H.S. = sin^2(pi/18)+sin^2((pi)/9)+sin^2((7pi)/18)+sin^2((4pi)/9)`
`=sin^2 10^@+ sin^2 20^@+ sin^2 70^@+sin^2 80^@`
`=sin^2 10^@+ sin^2 80^@+ sin^2 70^@+sin^2 20^@`
`=sin^2 10^@+ sin^2 (90-10)^@+ sin^2 (90-20)^@+sin^2 20^@`
`=(sin^2 10^@+ cos^2 10^@)+ (cos^2 20^@+sin^2 20^@)`
`=1+1= 2 = R.H.S.`


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