মান নির্ণয়

tanA.tan(60°+A).tan(120°+A)=?\tan{A}.tan (60°+A).tan(120°+A)=?

tanA.tan(60°+A)tan{180°(60°A)}=tanA.tan(60°+A).tan(60°A)=tanA.tan60°+tanA1tan60°tanA.tan60°tanA1+tan60°.tanA=tanA3+tanA13tanA.3tanA1+3tanA=tanA3tan2A13tan2A=3tanAtan3A13tan2A=tan3A \tan{A}.tan(60°+A)tan\{180°-(60°-A)\} \\ =-tanA.tan(60°+A).tan(60°-A)\\ =-tanA.\frac{tan60°+tanA}{1-tan60°tanA}.\frac{tan60°-tanA}{1+tan60°.tanA} \\ =-\tan{A}\frac{\sqrt3+\tan{A}}{1-\sqrt3\tan{A}}.\frac{\sqrt3-\tan{A}}{1+\sqrt3\tan{A}} \\ =-\tan{A}\frac{3-\tan^2{A}}{1-3\tan^2{A}}\\ =-\frac{3\tan{A}-\tan^3{A}}{1-3\tan^2{A}}=-\tan{3A}\

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