Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions5 Marks
Question
Prove that:
$\frac{\sin\text{A}+2\sin3\text{A}+\sin5\text{A}}{\sin3\text{A}+2\sin5\text{A}+\sin7\text{A}}=\frac{\sin3\text{A}}{\sin5\text{A}}$
✓

Answer

We have,

 $\text{LHS}=\frac{\sin\text{A}+2\sin3\text{A}+\sin5\text{A}}{\sin3\text{A}+2\sin5\text{A}+\sin7\text{A}}$

$=\ \frac{\sin5\text{A}+\sin\text{A}+2\sin3\text{A}}{\sin7\text{A}+\sin3\text{A}+2\sin5\text{A}}$

$=\ \frac{2\sin\Big(\frac{5\text{A}+\text{A}}{2}\Big)\cos\Big(\frac{5\text{A}-\text{A}}{2}\Big)+2\sin3\text{A}}{2\sin\Big(\frac{7\text{A}+3\text{A}}{2}\Big)\cos\Big(\frac{7\text{A}-3\text{A}}{2}\Big)+2\sin5\text{A}}$

$=\ \frac{2\sin3\text{A}\cos2\text{A}+2\sin3\text{A}}{2\sin5\text{A}\cos2\text{A}+2\sin5\text{A}}$

$=\ \frac{2\sin3\text{A}(\cos2\text{A}+1)}{2\sin5\text{A}(\cos2\text{A}+1)}$

$=\ \frac{\sin3\text{A}}{\sin5\text{A}}$

$=\ \text{RHS}$

$\frac{\sin\text{A}+2\sin3\text{A}+\sin5\text{A}}{\sin3\text{A}+2\sin5\text{A}+\sin7\text{A}}=\frac{\sin3\text{A}}{\sin5\text{A}}$  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→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If a, b, c, are in G.P., prove that the following are also in G.P.
$\text{a}^3,\text{b}^3,\text{c}^3$
→
Use the Principle of Mathematical Induction in the following Exercis.
We have a sequence d1, d2, d3 ....... defined by letting d1 = 2 and $\text{d}_\text{k}=\frac{\text{d}_{\text{k}-1}}{\text{k}},$ for all natural numbers $\text{k}\geq2.$ show that $\text{d}_\text{n}=\frac{2}{\text{n}!},$ for all $\text{n}\in\text{N}$ 
→
In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
The number of people who read at least one of the newspapers.
→
Find the coordinates of points on the parabola y2 = Bx whose focal distance is 4.
→
Prove that:
$\sin\frac{\text{x}}{2}\sin\frac{7\text{x}}{2}+\sin\frac{3\text{x}}{2}\sin\frac{11\text{x}}{2}=\sin2\text{x}\sin5\text{x}.$
→
In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E.
Then prove that,
  1. $\text{O}^2 – \text{E}^2 = (\text{x}^2 – \text{a}^2 )^\text{n}$
  2. $4\text{OE} = (\text{x} + \text{a})^{2\text{n}} – (\text{x} – \text{a})^{2\text{n}}$
→
Solve the following system of inequalities.
$\frac{2\text{x}+1}{7\text{x}-1}>5, \frac{\text{x}+7}{\text{x}-8}>2$
→
Solve the following system of equations in R.
$|\text{x}-1|+|\text{x}-2|+|\text{x}-3|\geq6$
→
Find the equation of the ellipse in the following case:

focus is (-1, 1), directrix is x - y + 3 = 0 and $\text{e}=\frac{1}{2}.$

→
Prove the following identities:
$\frac{1−\sin\text{x}\cos\text{x}}{\cos\text{x}(\sec\text{x}−\text{cosec}\text{x})}\cdot\frac{\sin^2\text{x}−\cos^2\text{x}}{\sin^3\text{x}\cos^3\text{x}}=\sin\text{x}$
→