[tex]\it Notez\ \ \dfrac{\pi}{7} = b,\ iar \ membrul \ st\hat{a}ng\ din\ egalitate \ devine:
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(sinb-cosa)^2 +(cosb-sina)^2 = sin^2b -2sinbcosa +cos^2a+cos^2 b -
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- 2sinacosb +sin^2a = (sin^2b+cos^2b)+(sin^2a+cos^2a) -
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-2(sinbcosa+sinacosb) [/tex]
Egalitatea din enunț devine : 2 -2(sinbcosa+sinacosb) = 2 ⇒
-2(sinbcosa+sinacosb) = 0 ⇒ sinbcosa+sinacosb = 0 ⇒ sin(b+a) =0 ⇒
⇒ b+a = π ⇒ a = π - b = π - π/7 = 6π/7