If $A+B+C=180^{\circ}$, then the value of $\tan A+\tan B+\tan C$ is

JEE MATHEMATICS MCQ: COMPOUND ANGLES

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A+B+C=180^{\circ}

, then the value of

\tan A+\tan B+\tan C

View answer and explanation

Correct option: A

\geq 3 \sqrt{3}

Option A (

\geq 3 \sqrt{3}

) is correct because when

A+B+C = 180^{\circ}

\tan A + \tan B + \tan C = \tan A \tan B \tan C

, and by AM-GM inequality, the minimum value is

3 \sqrt{3}

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\tan \left( {A + B} \right) = p

\tan \left( {A - B} \right) = q

\tan \,\,2A

\cos \,\,x\,\,\cos \,\,y\,\,\sin \,\,\left( {x - y} \right) + \cos \,\,y\,\,\cos \,\,z\,\,\sin \,\,\left( {y - z} \right)

+ \cos \,\,z\,\,\cos \,\,x\,\,\sin \,\,\left( {z - x} \right) + \sin \,\,\left( {x - y} \right)\sin \,\,\left( {y - z} \right)\,\,\sin \,\,\left( {z - x} \right)

\sin \alpha, \cos \alpha

\sqrt{1+\sin \alpha \cos \alpha}

0<\alpha<\frac{\pi}{2}

\tan \,\,A = 2\,\,\tan \,\,B + \cot \,\,B,\;\;\mathrm{then}\;\,2\,\,\tan \left( {A - B} \right)\mathrm{\;}

A,B,C

{\tan ^2}\,\,\frac{A}{2} + {\tan ^2}\,\,\frac{B}{2} + {\tan ^2}\,\,\frac{C}{2}

A > 0,\,\;B > 0

A + B = \frac{\pi }{3}

\tan A\,\,\tan B