Download App

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

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSSine And Cosine Formulae And Their Applications5 Marks
Question
$\text{a}(\cos\text{C}-\cos\text{B})=2(\text{b}-\text{c})\cos^2\frac{\text{A}}{2}.$
✓

Answer

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

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 "5 Marks Questions" 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

A circle whose centre is the point of intersection of the lines 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 passes through the origin. Find its equation.
→
Find the linear inequations for which the solution set is the shaded region given in Fig.
→
Prove that:
$\cot\frac{\pi}{8}=\sqrt{2}+1$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{5\text{x}+4\sin3\text{x}}{4\sin2\text{x}+7\text{x}}$
→
$\text{If}\ \text{y}\sin\phi=\text{x}\sin(2\theta+\phi),$ prove that $(\text{x+y})\cot(\theta+\phi)=(\text{y}-\text{x})\cot\theta$
→

If the seventh term from the beginning and in the binomial expansion of $\Big(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\Big)^{\text{n}}$ are equal, is the 7th term from the end.

→
Prove that:
$\frac{1}{\sin\text{(x}-\text{b})\sin\text{(x}-\text{b)}}=\frac{\cot\text{(x}-\text{b)}-\cot\text{(x}-\text{b)}}{\sin\text{(a}-\text{b)}}$
→
Prove that the following sets of three lines are concurrent:
3x - 5y - 11 = 0, 5x + 3y - 7 = 0 and x + 2y = 0
→
Let A, B and C be sets. Then show that $\text{A}\cap(\text{B}\cup\text{C})=(\text{A}\cap\text{B})\cup(\text{A}\cap\text{C}).$
→
Find the derivative of (sinx + cosx) from first principle.
→