In any , find the value of ( - ) - Vidyadip

Question

In any $\triangle\text{ABC},$ find the value of $\sum\text{a}(\sin\text{B}-\sin\text{C})$

✓

Answer

let $\text{a}\sin\text{B = b}\sin\text{A,b}\sin\text{C = c}\sin\text{A,a}\sin\text{C = c}\sin\text{A}$
$\sum\text{a}(\sin\text{B}-\sin\text{C})$
$=\text{a}(\sin\text{B}-\sin\text{C})+\text{b}(\sin\text{C}-\sin\text{A})+\text{c}(\sin\text{A}-\sin\text{B})$
$=\text{a}\sin\text{B}-\text{a}\sin\text{C + b}\sin\text{C}-\text{b}\sin\text{A + c}\sin\text{A}-\text{c}\sin\text{B}$
$=\text{b}\sin\text{A}-\text{a}\sin\text{C + b}\sin\text{C}-\text{b}\sin\text{A + a}\sin\text{C}-\text{b}\sin\text{C}$
$=0$

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 "1 Marks Question" 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

Write the distributive law for any three sets A, B and C.

In how many ways can 5 boys and 5 girls be seated around a round table such that no two girls sit together?

Determine whether the argument used to check the validity of the following statement is correct:
$p:$ "If $x^2$ is irrational, then x is rational"
The statement is true because the number $\text{x}^2=\pi^2$ is irrational, therefore $\text{x}=\pi$ is irrational.

Write the equations of directrix of a hyperbola

Find the limit: $\lim \limits_{x \rightarrow 1}\left[\frac{x-2}{x^{2}-x}-\frac{1}{x^{3}-3 x^{2}+2 x}\right]$

Let a sample space be S = {$\omega_1, \omega_2,..., \omega_6$}.Which of the following assignments of probabilities to each outcome are valid?

Outcomes	$\omega_1$	$\omega_2$	$\omega_3$	$\omega_4$	$\omega_5$	$\omega_6$
	$\frac 16$	$\frac 16$	$\frac 16$	$\frac 16$	$\frac 16$	$\frac 16$

Find the multiplicative inverse of the complex numbers -i

Translate the following statement into symbolic form:
2, 3 and 6 are factors of 12.

Check the validity of the following statements:
p: 100 is a multiple of 4 and 5.

If f is a real function satisfying $\text{f}\Big(\text{x}+\frac{1}{\text{x}}\Big)=\text{x}^2+\frac{1}{\text{x}^2}$ for all $\text{x}\in\text{R}-\{0\},$ then write the expression for f(x).