Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions5 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 Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Show that the set of all points such that the difference of their distances from (4, 0) and (-4, 0) is always equal to 2 represents a hyperbola
→
For any two sets of A and B, prove that:

$\text{A}'\cup\text{B}=\text{U}\Rightarrow\text{A}\subset\text{B.}$

→
$\Bigg|\sin\text{x}\sin\Big(\frac{\pi}{3}-\text{x}\Big)\sin\Big(\frac{\pi}{3}+\text{x}\Big)\Bigg|\not<\frac{1}{4}$ for all values of x.
→
Find the equation of the hyperbola whose
vertices are at $(\pm6, 0)$ and one of the directrices is x = 4
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow2}\frac{\sqrt{3+\text{x}}-1}{2-\text{x}}$
→
If $\sin\text{x}=\frac{12}{13}$ and x lies in the second quadrant, find the value of $\sec\text{x}+\tan\text{x}.$
→
Prove that:
$\sin3\text{A}+\sin2\text{A}-\sin\text{A}=4\sin\text{A}\cos\frac{\text{A}}{2}\cos\frac{3\text{A}}{2}$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-1}\frac{\text{x}^2-\text{x}-2}{\big(\text{x}^2+\text{x}\big)+\sin(\text{x}+1)}$
→
There are three independent witnesses of any event that has occurred. A speaks truth three times out of four times. B speaks truth four times out of five times and C speaks truth five times out of six times. What is the probability of all the witnesses speaking in favour of the event with majority?
→
Find three numbers in G.P. whose sum is 38 and their product is 1728.
→