Download App

Transformation Formulae — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTransformation Formulae4 Marks
Question
Prove that: $\frac{\cos3\text{A}+2\cos5\text{A}+\cos7\text{A}}{\cos\text{A}+2\cos3\text{A}+\cos5\text{A}}=\frac{\cos5\text{A}}{\cos3\text{A}}$
✓

Answer

We have, $\text{LHS}=\frac{\cos3\text{A}+2\cos5\text{A}+\cos7\text{A}}{2\cos\text{A}+2\cos3\text{A}+\cos5\text{A}}$ $=\ \frac{(\cos7\text{A}+\cos3\text{A})+2\cos5\text{A}}{(\cos5\text{A}+\cos\text{A})+2\cos3\text{A}}$ $=\ \frac{2\cos\Big(\frac{7\text{A}+3\text{A}}{2}\Big)\cos\Big(\frac{7\text{A}-3\text{A}}{2}\Big)+2\cos5\text{A}}{2\cos\Big(\frac{5\text{A}+\text{A}}{2}\Big)\cos\Big(\frac{5\text{A}-\text{A}}{2}\Big)+\cos3\text{A}}$ $=\ \frac{2\cos5\text{A}\cos2\text{A}+2\cos5\text{A}}{2\cos3\text{A}\cos2\text{A}+2\cos3\text{A}}$ $=\ \frac{2\cos5\text{A}(\cos2\text{A}+1)}{2\cos3\text{A}(\cos2\text{A}+1)}$ $=\ \frac{\cos5\text{A}}{\cos3\text{A}}$ $=\ \tan3\text{A}$ $=\ \text{RHS}$ $\therefore\ \frac{\cos3\text{A}+2\sin5\text{A}+\cos7\text{A}}{\cos\text{A}+2\cos3\text{A}+\cos5\text{A}}=\frac{\cos5\text{A}}{\cos3\text{A}}$ 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 "(Each question 4 marks)" from Transformation Formulae→Transformation Formulae — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Prove that: $\frac{\cos4\text{A}+\cos3\text{A}+\cos2\text{A}}{\sin4\text{A}+\sin3\text{A}+\sin2\text{A}}=\cot3\text{A}$
→
Evaluate the following limits in Exercise:$\lim\limits_{\text{x}\rightarrow\frac{\pi}{2}}\frac{\tan2\text{x}}{\text{x}-\frac{\pi}{2}}$
→
Sketch the graphs of the following functions: $\text{f(x)}=\cot2\text{x}$
→
Prove the following by the principle of mathematical induction: $1.3 + 2.4 + 3.5 + ... + \text{n}(\text{n} + 2) $ $=\frac{1}{6}\text{n}(\text{n}+1)(2\text{n}+7)$
→
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
  1. A particular professor is included.
  2. A particular student is included.
  3. A particular student is excluded.
→
Differentiate the following from the first principle$\sin\text{x}+\cos\text{x}$
→
Show that the origin is equidistant from the lines $4x + 3y + 10 = 0; 5x - 12y + 26 = 0$ and $7x + 24y = 50$.
→
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas: $y^2 + 4x + 4y - 3 = 0$
→
The coefficients of the $(r-1)^{\text {th }}, r^{\text {th }}$ and $(r+1)^{\text {th }}$ terms in the expansion of $(x+1)^n$ are in the ratio $1: 3: 5$. Find $n$ and $r$.
→
Convert the complex numbers given in Exercises in the polar form: $\sqrt{3}+\text{i}.$
→