Download App

Trigonometric Ratios Of Multiple And Sub Multiple Angles — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Multiple And Sub Multiple Angles5 Marks
Question
Prove that:
$\frac{1}{\sin\text{(x}-\text{b})\sin\text{(x}-\text{b)}}=\frac{\cot\text{(x}-\text{b)}-\cot\text{(x}-\text{b)}}{\sin\text{(a}-\text{b)}}$
✓

Answer

$\text{L.H.S}\ \frac{1}{\sin\text{(x}-\text{a)}\sin\text{(x}-\text{b)}}$
$=\frac{1}{\sin\text{(a}-\text{b)}}\Big[\frac{\sin\text{(a}-\text{b)}}{\sin\text{(x}-\text{b})\sin\text{(x}-\text{b)}}\Big]$
$=\frac{1}{\sin\text{(a}-\text{b)}}\Big[\frac{\sin\text{(x}-\text{b)-}(\text{x}-\text{b)}}{\sin\text{(x}-\text{a})\sin\text{(x}-\text{b)}}\Big]$
$=\frac{1}{\sin\text{(a}-\text{b)}}\Big[\frac{\sin\text{(x}-\text{b)}\cos(\text{x}-\text{a})-\cos(\text{x}-\text{b})\sin(\text{x}-\text{a)}}{\sin\text{(x}-\text{a})\sin\text{(x}-\text{b)}}\Big]$
$=\frac{1}{\sin\text{(a}-\text{b)}}\Big[\frac{\sin(\text{x}-\text{b)}\cos(\text{x}-\text{a})}{\sin\text{(x}-\text{a)}\sin(\text{x}-\text{b})}-\frac{\sin(\text{x}-\text{b)}\cos(\text{x}-\text{a})}{\sin\text{(x}-\text{a)}\sin(\text{x}-\text{b})}\Big]$
$=\frac{1}{\sin\text{(a}-\text{b)}}\Big[\cot(\text {x}-\text{a}-\cot(\text{x}-\text{b})\Big]$
$=\frac{\cot(\text{x}-\text{a})-\cot(\text{x}-\text{b})}{\sin(\text{a}-\text{b})}$
$=\text{R.H.S}$
$\therefore\ \text{L.H.S}=\text{R.H.S}$
Hence proved.

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 Ratios Of Multiple And Sub Multiple Angles→Trigonometric Ratios Of Multiple And Sub Multiple Angles — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-2}\frac{\text{x}^3+\text{x}^2+4\text{x}+12}{\text{x}^3+3\text{x}+2}$
→
If the lines p1x + q1y = 1, p2x + q2y = 1 and p3x + q3y = 1 be concurrent, show that the points (p1, q1), (p2, q2) and (p3, q3) are collinear.
→
If $\cos(\alpha+\beta)=\frac{4}{5}$ and $\sin(\alpha-\beta)=\frac{5}{13},$ where $\alpha$ lie between 0 and $\frac{\pi}{4},$ find the value of $\tan2\alpha$
$[$Hint: Express $\tan2\alpha$ as $\tan(\alpha+\beta+\alpha-\beta)]$
→
Let f, g : R → R be defined, respectively by f(x) = x + 1 and g(x) = 2x - 3. Find f + g, f - g and $\frac{\text{f}}{\text{g}}$
→
Prove that:
$(\text{A}\cap\text{B})\times\text{C}=(\text{A}\times\text{C})\cap(\text{B}\times\text{C})$
→
While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.
→
$\text{a}(\cos\text{B}+\cos\text{C}-1)+\text{b}(\cos\text{C}+\cos\text{A}-1)\\+\text{c}(\cos\text{A}+\cos\text{B}-1)=0$
→
A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be
  1. red
  2. yellow
  3. blue
  4. not blue
  5. either red or blue.
→
Find the standard deviation for the following data:
x
 2
3
4
5
6
 7
f
4
9
16
14
11
 6
→
Match the following sets for all sets A, B and C.
(i) $((\text{A}'\cup\text{B}')-\text{A})'$ (a) $\text{A} - \text{B}$
(ii) $[\text{B}'\cup(\text{B}'-\text{A})]'$ (b) $\text{A}$
(iii) $(\text{A} - \text{B}) - (\text{B} - \text{C})$ (c) $\text{B}$
(iv) $(\text{A}-\text{B})\cap(\text{C}-\text{B})$ (d) $(\text{A}\times\text{B})\cap(\text{A}\times\text{C})$
(v) $\text{A}\times(\text{B}\cap\text{C})$ (e) $(\text{A}\times\text{B})\cup(\text{A}\times\text{C})$
(vi) $\text{A}\times(\text{B}\cup\text{C})$ (f) $(\text{A}\cap\text{C})-\text{B}$
→