Download App

Transformation Formulae — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTransformation Formulae1 Mark
MCQ
If $\sin(\text{B+C}-\text{A}),\sin(\text{C+A}-\text{B}),\sin(\text{A+B}-\text{C})$ are in A.P., than $\cot\text{A},\cot\text{B},\cot\text{C}$ are in
  • A
    $\text{GP}$
  • ✓
    $\text{HP}$
  • C
    $\text{AP}$
  • D
    None of these
✓

Answer

Correct option: B.
$\text{HP}$
Given:
$\sin(\text{B+C}-\text{A}),\sin(\text{C+A}-\text{B}),\text{ and }\sin(\text{A+B}-\text{C})$ are in A.P.
$\Rightarrow\ \sin(\text{C+A}-\text{B})-\sin(\text{B+C}-\text{A})\\ \ \ \ =\sin(\text{A+B}-\text{C})-\sin(\text{C+A}-\text{B})$
$\Rightarrow\ 2\sin\Big(\frac{\text{C+A}-\text{B}-\text{B}-\text{C+A}}{2}\Big)\cos\Big(\frac{\text{C+A}-\text{B+B+C}-\text{A}}{2}\Big)\\ \ \ \ =2\sin\Big(\frac{\text{A+B}-\text{C}-\text{C}-\text{A+B}}{2}\Big)\cos\Big(\frac{\text{A+B}-\text{C+C+A}-\text{B}}{2}\Big)$
$\Rightarrow\ \sin(\text{A}-\text{B})\cos\text{C}=\sin(\text{B}-\text{C})\cos\text{A}$
$\Rightarrow\ \sin\text{A}\cos\text{B}\cos\text{C}-\cos\text{A}\sin\text{B}\cos\text{C}\\ \ \ =\sin\text{B}\cos\text{C}\cos\text{A}-\cos\text{B}\sin\text{C}\cos\text{A}$
$\Rightarrow\ 2\sin\text{B}\cos\text{A}\cos\text{C}=\sin\text{A}\cos\text{B}\cos\text{C}+\cos\text{A}\cos\text{B}\sin\text{C}$
Dividing both sides by $\cos\text{A}\cos\text{B}\cos\text{C}:$
$2\tan\text{B}=\tan\text{A}+\tan\text{C}$
$\Rightarrow\ \frac{2}{\cot\text{B}}=\frac{1}{\cot\text{A}}+\frac{1}{\cot\text{C}}$
Hence, $\cot\text{A}, \cot\text{B}\text{ and }\cot\text{C}$ are in H.P.

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 Transformation Formulae→Transformation Formulae — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If the sum of the coefficients of all the positive even powers of $x$ in the binomial expansion of $\left(2 x^{3}+\frac{3}{x}\right)^{10}$ is $5^{10}-\beta \cdot 3^{9}$, then $\beta$ is equal to
→
The complex number $\frac{{1 + 2i}}{{1 - i}}$ lies in which quadrant of the complex plane
→
The number of all possible positive integral values of $\alpha $ for which the roots of the quadratic equation, $6x^2 - 11x +\alpha =0$ are rational numbers is
→
If $1+\left(2+{ }^{49} C _{1}+{ }^{49} C _{2}+\ldots .+{ }^{49} C _{49}\right)\left({ }^{50} C _{2}+{ }^{50} C _{4}+\right.$ $\ldots . .+{ }^{50} C _{ so }$ ) is equal to $2^{ n } . m$, where $m$ is odd, then $n$ $+m$ is equal to.
→
A pair of tangents are drawn from the origin to the circle ${x^2} + {y^2} + 20(x + y) + 20 = 0$. The equation of the pair of tangents is
→
The domain of $f(x)=\frac{\log _{(x+1)}(x-2)}{e^{\log _e x}-(2 x+3)}, x \in R$ is
→
In a group of $15,7$ have studied German, $8$ have studied French, and $3$ have not studied either. How many of these have studied both German and French?
→
Suppose $\theta \in\left[0, \frac{\pi}{4}\right]$ is a solution of $4 \cos \theta-3 \sin \theta=1$ Then $\cos \theta$ is equal to :
→
Choose the correct answer. If the third term of $\text{G.P.}$ is $4,$ then the product of its first $5$ terms is:
→
If $\tan\alpha=\frac{1-\cos\beta}{\sin\beta},$ then:
→