Download App

Transformation Formulae — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTransformation Formulae4 Marks
Question
Prove that:
$\frac{\sin5\text{A}\cos2\text{A}-\sin6\text{A}\cos\text{A}}{\sin\text{A}\sin2\text{A}-\cos2\text{A}\cos3\text{A}}=\tan\text{A}$
✓

Answer

We have,
$\text{LHS}=\frac{\sin5\text{A}\cos2\text{A}-\sin6\text{A}\cos\text{A}}{\sin\text{A}\sin2\text{A}-\cos2\text{A}\cos3\text{A}}$
$=\ \frac{2(\sin5\text{A}\cos2\text{A}-\sin6\text{A}\cos\text{A})}{2(\sin\text{A}\sin2\text{A}-\cos2\text{A}\cos3\text{A})}$
$=\ \frac{2\sin5\text{A}\cos2\text{A}-2\sin6\text{A}\cos\text{A}}{2\sin\text{A}\sin2\text{A}-2\cos2\text{A}\cos3\text{A}}$
$=\ \frac{\sin(5\text{A}+2\text{A})+\sin(5\text{A}-2\text{A})-[\sin(6\text{A}+\text{A})+\sin(6\text{A}-\text{A})]}{\cos(2\text{A}-\text{A})-\cos(2\text{A}+\text{A})-[\cos(3\text{A}+2\text{A})+\cos(3\text{A}-2\text{A})]}$
$=\ \frac{\sin7\text{A}+\sin3\text{A}-\sin7\text{A}-\sin5\text{A}}{\cos\text{A}-\cos3\text{A}-\cos5\text{A}-\cos\text{A}}$
$=\ \frac{\sin3\text{A}-\sin5\text{A}}{-\cos3\text{A}-\cos5\text{A}}$
$=\ \frac{-(\sin5\text{A}-\sin3\text{A})}{-(\cos5\text{A}+\cos3\text{A})}$
$=\ \frac{\sin5\text{A}-\sin3\text{A}}{\cos5\text{A}+\cos3\text{A}}$
$=\ \frac{2\sin\Big(\frac{5\text{A}-3\text{A}}{2}\Big)\cos\Big(\frac{5\text{A}+3\text{A}}{2}\Big)}{2\cos\Big(\frac{5\text{A}+3\text{A}}{2}\Big)\cos\Big(\frac{5\text{A}-3\text{A}}{2}\Big)}$
$=\ \frac{\sin\text{A}\cos4\text{A}}{\cos4\text{A}\cos\text{A}}$
$=\ \frac{\sin\text{A}}{\cos\text{A}}$
$=\ \tan\text{A}$
$=\ \text{RHS}$
$\therefore\ \frac{\sin5\text{A}\cos2\text{A}-\sin6\text{A}\cos\text{A}}{\sin\text{A}\sin2\text{A}-\cos2\text{A}\cos3\text{A}}=\tan\text{A}$ 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 "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

In each of the following find the equations of the hyperbola satisfying the given conditions:Vertices $(\pm2, 0)$, foci $(\pm3, 0)$ [NCERT]
→
Evaluate the following limit:
$\lim\limits_{\text{n}\rightarrow\infty}{\Big(\frac{1}{\text{n}^2}+\frac{2}{\text{n}^2}+\frac{3}{\text{n}^2}+\ \cdots+\frac{\text{n}-1}{\text{n}^2}}{}\Big)$
→
Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that either both are black or both are kings.
→
If a, b, c, are in G.P., prove that the following are also in G.P.
$\text{a}^2,\text{b}^2,\text{c}^2$
→
Find the value of $\frac{3+\log _{10} 343}{2+\frac{1}{2} \log _{10}\left(\frac{49}{4}\right)+\frac{1}{2} \log _{10}\left(\frac{1}{25}\right)}$
→
Prove that the lines 2x - 3y + 1 = 0, x + y = 3, 2x - 3y = 2 and x + y = 4 form a parallelogram.
→
A man arranges to pay off a debt of ₹ 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
→
Evaluate the following limit:
$\lim\limits_{\text{h}\rightarrow0}\frac{\text{(a}+\text{h})^2\sin(\text{a}+\text{h})-\text{a}^2\sin\text{a}}{\text{h}}$
→
Find the equation of the hyperbola whose
Vertices are (-8, -1) and (-4, 4) and focus is (17, -1)
→
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE.
→