JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Analyzing +4 | -1

In a

\triangle A B C, \tan A \cdot \tan B \cdot \tan C=9

. For such triangles, if

\tan ^2 A+\tan ^2 B+\tan ^2 C=k

, then

View answer and explanation

Correct option: B

k>27

Option B (

k>27

) is correct because using the AM-GM inequality and the fact that

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

in a triangle, we can show that

\tan^2 A + \tan^2 B + \tan^2 C > 27

More Questions from TRIGONOMETRY RATIOS

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\tan \alpha=\frac{p}{q}

\alpha=6 \beta

\alpha

\frac{1}{2}[p \operatorname{cosec} 2 \beta-q \sec 2 \beta]

\cos 12^{\circ}+\cos 84^{\circ}+\cos 156^{\circ}+\cos 132^{\circ}

\triangle A B C

C

{\sin ^6}\,\,\theta + {\cos ^6}\,\,\theta + 3{\sin ^2}\,\,\theta \,\,{\cos ^2}\,\,\theta

\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}=

\sin ^2(A / 2)+\sin ^2(B / 2)-\sin ^2(C / 2)=