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
$\frac{\text{c}-\text{b}\cos\text{A}}{\text{b}-\text{c}\cos\text{A}}=\frac{\cos\text{B}}{\cos\text{C}}$
✓

Answer

$\frac{\text{c}-\text{b}\cos\text{A}}{\text{b}-\text{c}\cos\text{A}}=\frac{\cos\text{B}}{\cos\text{C}}$ $\text{LHS}=\frac{\text{c}-\text{b}\cos\text{A}}{\text{b}-\text{c}\cos\text{A}}$ $=\frac{\text{k}\sin\text{C}-\text{k}\sin\text{B}\cos\text{A}}{\text{k}\sin\text{B}-\text{k}\sin\text{C}\cos\text{A}}$ $=\frac{\sin(\pi-(\text{A + B}))-\sin\text{B}\cos\text{A}}{\sin(\pi(\text{A + C}))-\sin\text{C}\cos\text{A}}$ $=\frac{\sin(\text{A + B})-\sin\text{B}\cos\text{A}}{\sin(\text{A + C})-\sin\text{C}\cos\text{A}}$ $=\frac{\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}-\sin\text{B}\cos\text{A}}{\sin\text{A}\cos\text{C}+\cos\text{A}\sin\text{C}-\sin\text{C}\cos\text{A}}$ $=\frac{\sin\text{A}\cos\text{B}}{\sin\text{A}\cos\text{C}}$ $=\frac{\cos\text{B}}{\cos\text{C}}=\text{RHS}$

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

Find the coordinates of the orthocentre of the triangle whose vertices are (-1, 3), (2, -1) and (0, 0).
→
If $\text{f(x)}=\frac{\text{x}-1}{\text{x}+1},$ then show that:
  1. $\text{f}\Big(\frac{1}{\text{x}}\Big)=-\text{f(x)}$
  2. $\text{f}\Big(-\frac{1}{\text{x}}\Big)=-\frac{1}{\text{f(x)}}$
→
Find the equation of the straight lines passing through the following pair of points: (0, -a) and (b, 0)
→
Solve the following linear inequations in R: $\frac{\text{x}}{\text{x}-5}>\frac{1}{2}$
→
If the straight line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ passes through the point of intersection of the lines $x + y = 3$ and $2x - 3y = 1$ and is parallel to $x - y - 6 = 0$, find a and b.
→
Find the sum to n terms in each of the series in whose $n^{th}$ terms is given by $(2n - 1)^2$
→
Which term of the G.P.:$\frac13,\frac19,\frac{1}{17}\ ...\text{is}\frac{1}{19683}?$
→
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$36x^2 + 4y^2 = 144$
→
Solve the following system of equations in R. $|3-4\text{x}|\geq9$
→
Find the real values of x and y, if $(1+\text{i})(\text{x}+\text{iy})=2-5\text{i}$
→