c(a -b )=a^2-b^2 - Vidyadip

Question

$\text{c}(\text{a}\cos\text{B}-\text{b}\cos\text{A})=\text{a}^2-\text{b}^2$

✓

Answer

$\text{c}(\text{a}\cos\text{B}-\text{b}\cos\text{A})$
$=\text{ac}.\cos\text{B}-\text{bc}\cos\text{A}$
$=\text{ac}.\frac{\text{a}^2+\text{c}^2-\text{b}^2}{2\text{ac}}-\text{bc}.\frac{\text{b}^2+\text{c}^2-\text{a}^2}{2\text{bc}}$
$=\frac{\text{a}^2+\text{c}^2-\text{b}^2}{2}-\frac{\text{b}^2+\text{c}^2-\text{a}^2}{2}$
$=\frac{\text{a}^2+\text{c}^2-\text{b}^2-\text{b}^2-\text{c}^2+\text{a}^2}{2}$
$=\frac{2\text{a}^2-2\text{b}^2}{2}=(\text{a}^2-\text{b}^2)$

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 "3 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→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x - y + 9 = 0.

Find the equation of a line drawn perpendicular to the line $\frac{\text{x}}{4}+\frac{\text{y}}{6}=1$ through the point where it meets the y-axis.

Differentiate the following from first principles:

$\frac{2}{\text{x}}$

A sports team of 11 students is to be constituted, choosing at least 5 from Class XI and atleast 5 from Class XII. If there are 20 students in each of these classes, in how many ways can the team be constituted?

Let R be a relation from N to N defined by $\text{R}=\{(\text{a, b}):\text{a, b}\in\text{N and a}=\text{b}^2\}.$ Are the following statement true?
$(\text{a, b})\in\text{R }\Rightarrow \text{(b, a)}\in\text{R}$

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if:

They can be of any colour.
Two must be white and two red and.
They must all be of the same colour.

Differentiate the following functions.
$\frac{\text{x}^{2}\cos\frac{\pi}{4}}{\sin\text{x}}$

Find the values of the other five trigonometric functions in the following:
$\cot\text{x}=-\frac{1}{2},$ x in quadrant II

Find the length of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and C (6, 0, 0).

A dice is thrown twice. What is the probability that at least one of the two throws come up with the number 3?