Download App

Sine and Cosine Formulae and Their Applications — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSine and Cosine Formulae and Their Applications3 Marks
Question
$\text{b}(\text{c}\cos\text{A}-\text{a}\cos\text{C})=\text{c}^2-\text{a}^2$
✓

Answer

$\text{b}(\text{c}\cos\text{A}-\text{a}\cos\text{C})=\text{c}^2-\text{a}^2$$\text{RHS}=\text{c}^2-\text{a}^2$
$=\text{k}^2\sin^2\text{C}-\text{k}^2\sin^2\text{A}$
$=\text{k}^2(\sin^2\text{C}-\sin^2\text{A})$
$=\text{k}^2\sin(\text{C + A}).\sin(\text{C}-\text{A})$
$=\text{k}^2\sin(\pi-\text{B}).\sin(\text{C}-\text{A})$
$=\text{k}^2\sin\text{B}.\sin(\text{C}-\text{A})$
$=\text{k}\sin\text{B}.\text{k}\sin(\text{C}-\text{A})$
$=\text{bk}\sin(\text{C}-\text{A})$
$=\text{bk}(\sin\text{C}.\cos\text{A}-\sin\text{A}.\cos\text{C})$
$=\text{b}(\text{k}\sin\text{C}.\cos\text{A}-\text{k}\sin\text{A}.\cos\text{C})$
$=\text{b}(\text{c}\cos\text{A}-\text{a}\cos\text{C})=\text{LHS}$

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 "(Each question 3 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→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Insert six A.M.s between $15$ and $−13$.
→
Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle $\tan^{-1}\Big(\frac{5}{12}\Big)$ with the positive direction of x-axis.
→
Show that the points $(3, -2), (1, 0), (-1, -2)$ and $(1, -4)$ are concyclic.
→
If $\sin\text{A}=\frac{4}{5}$ and $\cos\text{B}=\frac{5}{13}$ Where $0<\text{A},\text{B}<\frac{\pi}{2},$ find the value of the following:
→
Prove that: $\cot^2\text{x}-\tan^2\text{x}=4\cot2\text{x}\ \text{cosec}\ 2\text{x}$
→
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
→
Prove that: $4(\cos^310^\circ+\sin^320^\circ)=3(\cos10^\circ+\sin20^\circ)$
→
If $\text{y}=\frac{\text{2x}^9}{3}-\frac{\text{5x}^7}{7}+\text{6x}^3-\text{x},$ find $\frac{\text{dy}}{\text{dx}}$ at $\text{x}=1$
→
Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.
→
Find the ratio in which the sphere $x^2 + y^2 + z^2 = 504$ divides the line joining the points $(12, -4, 8)$ and $(21, -9, 18)$.
→