Advertisements
Advertisements
प्रश्न
If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=
पर्याय
- \[\frac{m - 1}{m + 1}\]
- \[\frac{m + 2}{m - 2}\]
- \[\frac{m + 1}{m - 1}\]
None of these
उत्तर
Given:
\[\cos A = m\cos B\]
\[ \Rightarrow \frac{\cos A}{\cos B} = \frac{m}{1}\]
\[ \Rightarrow \frac{\cos A + \cos B}{\cos A - \cos B} = \frac{m + 1}{m - 1}\]
\[ \Rightarrow \frac{2\cos\left( \frac{A - B}{2} \right)\cos\left( \frac{A + B}{2} \right)}{- 2\sin\left( \frac{B + A}{2} \right)\sin\left( \frac{B - A}{2} \right)} = \frac{m + 1}{m - 1} \left[ \because \cos A + \cos B = 2\cos\left( \frac{A - B}{2} \right)\cos\left( \frac{A + B}{2} \right) \text{ and }\cos A - \cos B = 2\sin\left( \frac{A + B}{2} \right)\cos\left( \frac{B - A}{2} \right) \right]\]
\[ \Rightarrow \frac{\cos\left( \frac{B - A}{2} \right)\cos\left( \frac{A + B}{2} \right)}{\sin\left( \frac{A + B}{2} \right)\sin\left( \frac{B - A}{2} \right)} = \frac{m + 1}{m - 1} \]
\[ \Rightarrow \cot\left( \frac{A + B}{2} \right)\cot\left( \frac{B - A}{2} \right)=\frac{m + 1}{m - 1}\]
APPEARS IN
संबंधित प्रश्न
Prove that:
Show that :
Prove that tan 20° tan 30° tan 40° tan 80° = 1.
Prove that:
sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
Show that:
sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0
Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
Prove that
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]
If α + β = \[\frac{\pi}{2}\], show that the maximum value of cos α cos β is \[\frac{1}{2}\].
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
sin 50° + sin 10° = cos 20°
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
Prove that:
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
cos (A + B + C) + cos (A − B + C) + cos (A + B − C) + cos (− A + B + C) = 4 cos A cos Bcos C
If cosec A + sec A = cosec B + sec B, prove that tan A tan B = \[\cot\frac{A + B}{2}\].
If (cos α + cos β)2 + (sin α + sin β)2 = \[\lambda \cos^2 \left( \frac{\alpha - \beta}{2} \right)\], write the value of λ.
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
Write the value of the expression \[\frac{1 - 4 \sin 10^\circ \sin 70^\circ}{2 \sin 10^\circ}\]
If A + B = \[\frac{\pi}{3}\] and cos A + cos B = 1, then find the value of cos \[\frac{A - B}{2}\].
Write the value of \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]
Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]
If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos2 (θ − ϕ) =
The value of cos 52° + cos 68° + cos 172° is
sin 47° + sin 61° − sin 11° − sin 25° is equal to
If sin (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in
Express the following as the sum or difference of sine or cosine:
cos 7θ sin 3θ
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
Find the value of tan22°30′. `["Hint:" "Let" θ = 45°, "use" tan theta/2 = (sin theta/2)/(cos theta/2) = (2sin theta/2 cos theta/2)/(2cos^2 theta/2) = sintheta/(1 + costheta)]`
If secx cos5x + 1 = 0, where 0 < x ≤ `pi/2`, then find the value of x.
