Download App

Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions5 Marks
Question
Prove that:
$\frac{\sin\text{A}+\sin\text{B}}{\sin\text{A}-\sin\text{B}}=\tan\Big(\frac{\text{A}-\text{B}}{2}\Big)\cot\Big(\frac{\text{A}-\text{B}}{2}\Big)$
✓

Answer

We have,
$\text{LHS}=\frac{\sin\text{A}+\sin\text{B}}{\sin\text{A}-\sin\text{B}}$
$=\ \frac{2\sin\Big(\frac{\text{A}+\text{B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}{2\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)}$
$=\ \frac{\sin\Big(\frac{\text{A}+\text{B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}{\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)}$
$= \tan\Big(\frac{\text{A+B}}{2}\Big)\cot\Big(\frac{\text{A}-\text{B}}{2}\Big)$
$=\ \text{RHS}$
$\therefore\ \frac{\sin\text{A}+\sin\text{B}}{\sin\text{A}-\sin\text{B}}=\tan\Big(\frac{\text{A+B}}{2}\Big)\cot\Big(\frac{\text{A}-\text{B}}{2}\Big).$ 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 Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
→
If a, b, c, d are in G.P., prove that:
$(\text{a}+\text{b}+\text{c}+\text{d})^2=(\text{a}+\text{b}^2)+2(\text{b}+\text{c})^2+(\text{c}+\text{d})^2$
→
How many permutations can be formed by the letters of the word, $\text{'VOWELS',}$ when.
  1. There is no restriction on letters?
  2. Each word begins with $E?$
  3. Each word begins with $O$ and ends with $L?$
  4. All vowels come together$?$
  5. All consonants come together$?$
→
Name the octant in which each of the following points lies:
  1. $(1, 2, 3).$
  2. $(4, -2, 3).$
  3. $(4, -2, -5).$
  4. $(4, 2, -5).$
  5. $(-4, 2, 5).$
  6. $(-3, -1, 6).$
  7. $(2, -4, -7).$
  8. $(-4, 2, -5).$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}(1-\text{x})\tan\Big(\frac{\pi\text{x}}{2}\Big)$
→
Find the equation of the parabola, if
The focus is at (0, 0) and vertex is at the intersection of the lines x + y = 1 and x - y = 3.
→
A sequence $x_1, x_2, x_3, ...$ is defined by letting $x_1 = 2$ and $\text{x}_{\text{k}}=\frac{\text{x}_{\text{k}}-1}{\text{n}}$ for all natural numbers k, $\text{k}\geq2.$ Show that $\text{x}_{\text{n}}=\frac{2}{\text{n}!}$ for all $\text{n}\in\text{N}.$
→
Two ships leave a port at the same time. One goes 24km/ hr in the direction N 38° E and other travels 32km/ hr in the direction S 52° E. Find the distance between the ships at the end of 3hrs.
→
Calculate the mean, median and standard deviation of the following distribution:
Class-interval: 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70
Frequency: 2 3 8 12 16 5 2 3
→
Prove that:
$\cos\text{x}\cos\frac{\text{x}}{2}-\cos3\text{x}\cos\frac{9\text{x}}{2}=\sin7\text{x}\sin8\text{x}.$
→