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Prove that: sin^2(pi/18)+sin^2(pi/9)+sin...

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

Text Solution

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`sin^2.pi/18+sin^2.pi/9+sin^2.(7pi)/18+sin^2. (4pi)/9`
`=sin^2.pi/18+sin^2.pi/9+sin^2. ((pi)/2-pi/9)+sin^2(pi/2-pi/18)`
`=sin^2. pi/18+sin^2. pi/9+cos^2 .pi/9+cos^2. pi/18`
`=(sin^2. pi/18+cos^2. pi/18)+(sin^2. pi/9+cos^2. pi/9)=2`
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