Download App

Transformation Formulae — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTransformation Formulae4 Marks
Question
Prove that:
$\sin3\text{A}+\sin2\text{A}-\sin\text{A}=4\sin\text{A}\cos\frac{\text{A}}{2}\cos\frac{3\text{A}}{2}$
✓

Answer

We have,
$\text{LHS}=\sin3\text{A}+\sin2\text{A}-\sin\text{A}$
$=\ \sin3\text{A}-\sin\text{A}+\sin2\text{A}$
$=\ 2\sin\Big(\frac{3\text{A}-\text{A}}{2}\Big)\cos\Big(\frac{3\text{A}+\text{A}}{2}\Big)+\sin2\text{A}$
$=\ 2\sin\text{A}\cos2\text{A}+\sin2\text{A}$
$=\ 2\sin\text{A}\cos2\text{A}+2\sin\text{A}\cos\text{A}$
$=\ 2\sin\text{A}[\cos2\text{A}+\cos\text{A}]$
$=\ 2\sin\text{A}\Big[2\cos\Big(\frac{2\text{A}+\text{A}}{2}\Big)\cos\Big(\frac{2\text{A}-\text{A}}{2}\Big)\Big]$
$=\ 4\sin\text{A}\cos\frac{3\text{A}}{2}\cos\frac{\text{A}}{2}$
$=\ 4\sin\text{A}\cos\frac{\text{A}}{2}\cos\frac{3\text{A}}{2}$
$=\ \text{RHS}$
$\therefore\ \sin3\text{A}+\sin2\text{A}-\sin\text{A}=4\sin\text{A}\cos\frac{\text{A}}{2}\cos\frac{3\text{A}}{2}.$
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 "Solve the Following Question.(4 Marks)" from Transformation Formulae→Transformation Formulae — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If a circle passes through the point (0, 0),(a, 0),(0, b) then find the coordinates of its centre.
→
Prove by the method of induction, for all n ∈ N.

$1.3+3.5+5.7+\ldots$ to $n$ terms $=\frac{n}{3}\left(4 n^2+6 n-1\right)$

→
Express the following complex numbers in the form $\text{r}(\cos\theta+\text{i}\sin\theta):$
$\frac{1-\text{i}}{\cos\frac{\pi}{3}+\text{i}\sin\frac{\pi}{3}}$
→
The $4^{\text {th }}$ and $7^{\text {th }}$ terms of G.P. are $\frac{1}{27}$ and $\frac{1}{729}$ respectively. Find the sum of $n$ terms of the G.P.
→
Find the trigonometric functions of $: 210^\circ$
→
Find the square roots of
6 + 8i
→
Prove that:
$\frac{\sin11\text{A}\sin\text{A}+\sin7\text{A}\sin3\text{A}}{\cos11\text{A}\sin\text{A}+\cos7\text{A}\sin3\text{A}}=\tan8\text{A}$
→
Sketch the graphs of the following pairs of functions on the same axes:
$\text{f(x)}=\sin\frac{\text{x}}{2},\text{g(x)}=\sin\text{x}$
→
Prove that:
$\cot\frac{\pi}{8}=\sqrt{2}+1$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-2}\frac{\text{x}^3+\text{x}^2+4\text{x}+12}{\text{x}^3+3\text{x}+2}$
→