Download App

Transformation Formulae — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTransformation Formulae3 Marks
Question
Prove that:
$\frac{\sin\text{A}-\sin\text{B}}{\cos\text{A}+\cos\text{B}}=\tan\frac{\text{A}-\text{B}}{2}$
✓

Answer

We have,
$\text{LHS}=\frac{\sin\text{A}-\sin\text{B}}{\cos\text{A}+\cos\text{B}}$
$=\ \frac{2\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)}{2\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}$
$=\ \frac{\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)}{\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}$
$= \tan\Big(\frac{\text{A}-\text{B}}{2}\Big)$
$=\ \text{RHS}$
$\therefore\ \frac{\sin\text{A}-\sin\text{B}}{\cos\text{A}+\cos\text{B}}=\tan\Big(\frac{\text{A}-\text{B}}{2}\Big).$ 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 "Solve the Following Question.(3 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 $\sin\text{A}=\frac{4}{5}$ and $\cos\text{B}=\frac{5}{13}$ Where $0<\text{A},\text{B}<\frac{\pi}{2}$,find the value of the following:
→
Sketch the graphs of the following function:
$\text{u(x)}=\sin^2\text{x},0\leq\text{x}\leq2\pi$
$\text{v(x)}=|\sin\text{x}|,0\leq\text{x}\leq2\pi$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sqrt{1+\text{x}}-\sqrt{1-\text{x}}}{2\text{x}}$
→
The ratio of the sum of first three term is to that of first $6$ terms of a G.P. is $125 : 152$. Find the common ratio.
→
Find the sum of the following geometric series:
$\sqrt{7},\sqrt{21},3\sqrt{7},\dots\text{to n terms}$
→
Show the following quadratic equation by factorization method:
$17x^2 - 28x + 12 = 0$
→
Find the square root of the following complex numbers:7 + 24i
→
Prove that: $\tan36^\circ+\tan9^\circ+\tan36^\circ+\tan9^\circ=1$
→
Differentiate the following w.r.t. x :$y=\frac{x e^x}{x+e^x}$
→
Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x - 3y = 7.
→