Download App

Sine And Cosine Formulae And Their Applications — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSine And Cosine Formulae And Their Applications1 Mark
MCQ
In any $\triangle\text{ABC},\sum\text{a}^2(\sin\text{B}-\sin\text{C})=$
  • A
    $\text{a}^2+\text{b}^2+\text{c}^2$
  • B
    $\text{a}^2$
  • C
    $\text{b}^2$
  • ✓
    $0$
✓

Answer

Correct option: D.
$0$
Using sine rule, we have
$\sum\text{a}^2(\sin\text{B}-\sin\text{C})$
$\text{a}^2\Big(\frac{\text{b}}{\text{k}}-\frac{\text{c}}{\text{k}}\Big)+\text{b}^2\Big(\frac{\text{c}}{\text{k}}-\frac{\text{a}}{\text{k}}\Big)+\text{c}^2\Big(\frac{\text{a}}{\text{k}}-\frac{\text{b}}{\text{k}}\Big)$
$=\frac{1}{\text{k}}(\text{a}^2\text{b}-\text{a}^2\text{c}+\text{b}^2\text{c}-\text{b}^2\text{a}+\text{c}^2\text{a}-\text{c}^2\text{b})$
This expression cannot be simplified to match with any of the given options.
However, if the quesion is "In any $\triangle\text{ABC},\sum\text{a}^2(\sin\text{B}-\sin\text{C})=",$ then the solution is as follows.
Using sine rule, we have
$\sum\text{a}^2(\sin^2\text{B}-\sin^2\text{C})$
$\text{a}^2\Big(\frac{\text{b}^2}{\text{k}^2}-\frac{\text{c}^2}{\text{k}^2}\Big)+\text{b}^2\Big(\frac{\text{c}^2}{\text{k}^2}-\frac{\text{a}^2}{\text{k}^2}\Big)+\text{c}^2\Big(\frac{\text{a}^2}{\text{k}^2}-\frac{\text{b}^2}{\text{k}^2}\Big)$
$\frac{1}{\text{k}^2}(\text{a}^2\text{b}^2-\text{a}^2\text{c}^2+\text{b}^2\text{c}^2-\text{b}^2\text{a}^2+\text{c}^2\text{a}^2-\text{c}^2\text{b}^2)$
$=\frac{1}{\text{k}^2}\times0$
$=0$
Hence, the correct answer is option (d).

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 Sine And Cosine Formulae And Their Applications→Sine And Cosine Formulae And Their Applications — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The sum of the real values of $x$ for which the middle term in the binomial expansion of ${\left( {\frac{{{x^3}}}{3} + \frac{3}{x}} \right)^8}$ equals $5670$ is
→
If $\mathop {\lim }\limits_{x \to 2} \frac{{a{x^2} + bx + c}}{{{{(2x - 1)}^2}}} = \frac{1}{2}$ then $\mathop {\lim }\limits_{x \to 2} \frac{{(x - a)(x - b)(x - c)}}{{x - 2}}$ is
→
If $\omega $ is a complex cube root of unity, then$225+$${{(3\omega +8{{\omega }^{2}})}^{2}}$$+{{(3{{\omega }^{2}}+8\omega )}^{2}}=$ [EAMCET 2003]
→
The number of words from the letters of the word $'\text{BHARAT}'$ in which $B$ and $H$ will never come together, is:
→
An ellipse passes through the point $(-3, 1)$ and its eccentricity is $\sqrt {\frac{2}{5}} $. The equation of the ellipse is
→
If $\alpha$ and $\beta $ are roots of ${x^2} - 3x + 1 = 0,$ then the equation whose roots are $\frac{1}{{\alpha - 2}},\frac{1}{{\beta - 2}}$ is
→
The median of all $4-$digit numbers that are divisible by $7$ is
→
If $\omega (\ne 1)$ is a cube root of unity, then $\left| \begin{matrix}    1 & 1+i+{{\omega }^{2}} & {{\omega }^{2}}  \\    1-i & -1 & {{\omega }^{2}}-1  \\    -i & -i+\omega -1 & -1  \\ \end{matrix} \right|$ is equal to [IIT 1995]
→
The number $111......1 $ ( $ 91$ times) is
→
Let $L(m)$ be the $x-$ coordinate of the left end point of the intersection of the graphs of $y = x^2 - 6$ and $y = m$ , where $-6 < m < 6$ . The value of $\mathop {\lim }\limits_{m \to 0} \left( {\frac{{L\left( { - m} \right) - L\left( m \right)}}{m}} \right)$ equals
→