Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions5 Marks
Question
$\frac{\text{a}^2\sin(\text{B}-\text{C})}{\sin\text{A}}+\frac{\text{b}^2\sin(\text{C}-\text{A})}{\sin\text{B}}+\frac{\text{c}^2\sin(\text{A}-\text{B})}{\sin\text{C}}=0$
✓

Answer

$\frac{\text{a}^2\sin(\text{B}-\text{C})}{\sin\text{A}}+\frac{\text{b}^2\sin(\text{C}-\text{A})}{\sin\text{B}}+\frac{\text{c}^2\sin(\text{A}-\text{B})}{\sin\text{C}}=0$
$\frac{\text{a}}{\sin\text{A}}=\frac{\text{b}}{\text{b}\sin\text{C}}=\frac{\text{c}}{\sin\text{C}}=\text{k}$
$\text{LHS}=\frac{\text{a}^2\sin(\text{B}-\text{C})}{\sin\text{A}}+\frac{\text{b}^2\sin(\text{C}-\text{A})}{\sin\text{B}}+\frac{\text{c}^2\sin(\text{A}-\text{B})}{\sin\text{C}}$
$=\text{ak}\sin(\text{B}-\text{C})+\text{bk}\sin(\text{C}-\text{A})+\text{ck}\sin(\text{A}-\text{B})$
$=\sin\text{A}\sin(\text{B}-\text{C})+\sin\text{B}\sin(\text{C}-\text{A})+\sin(\text{A}-\text{B})$
$=\sin(\pi-(\text{B + C}))\sin(\text{B}-\text{C})+\sin(\pi-(\text{C + A}))\\\sin(\text{C}-\text{A})+\sin(\pi-(\text{A + B}))\sin(\text{A}-\text{B})$
$=\sin(\text{B + C})\sin(\text{B}-\text{C})+\sin(\text{C + A})\\\sin(\text{C} - \text{A})+\sin(\text{A + B})\sin(\text{A}-\text{B})$
$=\sin^2\text{B}-\sin^2\text{C}+\sin^2\text{C}-\sin^2\text{A}+\sin^2\text{A}-\sin^2\text{B}=0=\text{RHS}$

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

$\Bigg|\sin\text{x}\sin\Big(\frac{\pi}{3}-\text{x}\Big)\sin\Big(\frac{\pi}{3}+\text{x}\Big)\Bigg|\not<\frac{1}{4}$ for all values of x.
→
If P(11, r) = P(12, r − 1) find r.
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow7}\frac{4-\sqrt{9+\text{x}}}{1-\sqrt{8-\text{x}}}$
→
An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that
  1. Both the balls are red.
  2. One ball is red and the other is black.
  3. One ball is white.
→
Use the Principle of Mathematical Induction in the following Exercis.
Prove that: $\sin\theta+\sin2\theta+\sin3\theta+\ ....\ +\sin\text{n}\theta=\frac{\sin\frac{\text{n}\theta}{2}\cdot\sin\frac{\text{n}+1}{2}\theta}{\sin\frac{\theta}{2}},$ for all $\text{n}\in\text{N}.$ 
→
For any two sets A and B, prove the following:
$\text{A} - \text{B}=\text{A }\Delta\text{ (A}\cap\text{B})$
→
Reduce each of the following expressions to the sine and cosin of a single expression:
$\cos\text{x}-\sin\text{x}$
→
Differentiate the following from first principle

$\sin\sqrt{2\text{x}}$

→
Show that the straight lines given by (2 + k)x + (1 + k)y = 5 + 7k for different values of k pass through a fixed point. Also, find that point.
→
For three sets A, B and C, show that.
$\text{A}\subset\text{B}\Rightarrow\text{C}-\text{B}\subset\text{C}-\text{A}.$
→