If in a , + + =0, then = - Vidyadip

MCQ

If in a $\Delta\text{ABC},\tan\text{A}+\tan\text{B}+\tan\text{C=0,}$ then $\cot\text{A}\cot\text{B}\cot\text{C}=$

A
$6$
B
$1$
C
$\frac{1}{6}$
D
None of these

✓

Answer

None of these

Solution:

ABC is a tringle.

$\therefore\text{A}+\text{B}+\text{C}=\pi$

$\Rightarrow\text{A}+\text{B}+\pi-\text{C}$

$\Rightarrow\tan(\text{A}+\text{B})=\tan(\pi-\text{C})$

$\Rightarrow\frac{\tan\text{A}+\tan\text{B}}{1-\tan\text{A}\tan\text{B}}=-\tan\text{C}$

$\Rightarrow\tan\text{A}+\tan\text{B}=-\tan\text{C}+\tan\text{A}\tan\text{B}\tan\text{C}$

$\Rightarrow\tan\text{A}+\tan\text{B}+\tan\text{C}=\tan\text{A}\tan\text{B}\tan\text{C}$

$\Rightarrow0=\tan\text{A}+\tan\text{B}\tan\text{C}$ $\big[$ given: $\tan\text{A}\tan\text{B}\tan\text{C}=0\big]$

$\Rightarrow\tan\text{A}\tan\text{B}\tan\text{C}=0$

$\Rightarrow\frac{1}{\tan\text{A}\tan\text{B}\tan\text{C}}=\frac{1}{0}$

$\Rightarrow\cot\text{A}\cot\text{B}\cot\text{C}\rightarrow\infty$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

The sum of the infinity of the series 1+2/3 + 6/32 + 10/33 +14/34 is:

Choose the correct answer.
$\lim\limits_{\text{x} \rightarrow0}\frac{\text{x}^{\text{m}}-1}{\text{x}^{\text{n}}-1}$ is equal to:

If A and B are two disjoint sets, then $\text{n(A}\cup\text{B)}$ is equal to:

$\text{n(A) + n(B)}$
$\text{n(A) + n(B)} - \text{n(A}\cap\text{B)}$
$\text{n(A) + n(B) + n(A}\cap\text{B)}$
$\text{n(A) n(B)}.$

The wickets taken by a bowler in a one day cricket match are 4, 5, 6, 3, 4, 0, 3, 2, 3, 5. The mode of the data is ________ .

If $\frac{1}{x}+x=2\cos \theta ,$ then ${{x}^{n}}+\frac{1}{{{x}^{n}}}$ is equal to [UPSEAT 2001]

Two functions f and g are said to be equal if:

If the point $(\lambda,\ \lambda+1)$ lies inside the region bounded by the curve $\text{x}=\sqrt{25-\text{y}^2}$ and y-axis, then $\lambda$ belongs to the interval:

If $f(x)=\frac{x^n-a^n}{x-a}$ for some constant, a, then $f ^{\prime}(a)$ is equal to

A complex number is pure imaginary if:

If $\frac{3\pi}{4}<\text{a}<\pi,$ then $\sqrt{2\cot\text{a}+\frac{1}{\sin^\text{a}}}$ is equal to:

$1-\cot\text{a}$
$1+\cot\text{a}$
$-1+\cot\text{a}$
$-1-\cot\text{a}$