Download App

Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions1 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:
$\sin(\text{B+C}-\text{A}),\sin(\text{C+A}-\text{B}),$ 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, $\cot\text{A}, \cot\text{B}$ 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 Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The average weight of students in a class of $35$ students is $40\ kg$. If the weight of the teacher be included, the average rises by $\frac{1}{2}$ $kg$; the weight of the teacher is.....$kg$
→
Let $P (n)$ be the statement $3n > nn.$ If $P (n)$ is true, then $P (n + 1)$ is
→
$(\sqrt{5}+1)^4+(\sqrt{5}-1)^4$ is
→
The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4 x-5 y=20$ to the circle $x^2+y^2=9$ is
→
If the first and the second letters of the word $\text{MISJUDGEMENTS}$ are interchanged with the last and the second last letters respectively, and similarly the third and the fourth letters are interchanged with the third and the fourth letters from the last respectively , and so on,then what will be the fifth letter to the right of the third letter from the left end?
→
The locus of the poles of normal chords of an ellipse is given by
→
If $A$ denotes the sum of all the coefficients in the expansion of $\left(1-3 x+10 x^2\right)^n$ and $B$ denotes the sum of all the coefficients in the expansion of $\left(1+x^2\right)^n$, then :
→
If sum of all the coefficients in the expansion of $\Big(\text{x}^{\frac{3}{2}}+\text{x}^{\frac{1}{3}}\Big)^{\text{n}}$ is $128$, then the coefficient of $x^5$ is:
→
Domain of the function $\frac{{\sqrt {1 + x} - \sqrt {1 - x} }}{x}$ is
→
The line joining two points $A(2,0), B(3,1)$ is rotated about $A$ in anti-clockwise direction through an angle of ${15^o}$. The equation of the line in the new position, is
→