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If 0 lt alphalt beta lt gamma lt pi//2, then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has |
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Answer» real and unequal ROOTS Now, `f(sin ALPHA)=(sinalpha-sinbeta)(sinalpha-singamma)` `=(-)(-)=positive `f(sinbeta)=(sinbeta-sinalpha)(sinbeta-sinalpha)=(+)(-)=`negative `f(sin gamma)=(sin gamma-sinalpha)(singamma-sinbeta)=(+)(+)=`positive `IMPLIES "Roots of " f(x)=0` are real and distinct. |
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