Advertisements
Advertisements
प्रश्न
If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=
विकल्प
- \[\frac{m - 1}{m + 1}\]
- \[\frac{m + 2}{m - 2}\]
- \[\frac{m + 1}{m - 1}\]
None of these
Advertisements
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:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]
Prove that:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
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
Express each of the following as the product of sines and cosines:
cos 12x - cos 4x
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
sin 50° − sin 70° + sin 10° = 0
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
Prove that:
Prove that:
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A
Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]
Prove that:
Prove that:
Prove that:
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), prove that tan A tan B tan C + tan D = 0.
Write the value of the expression \[\frac{1 - 4 \sin 10^\circ \sin 70^\circ}{2 \sin 10^\circ}\]
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 sin 50° − sin 70° + sin 10° 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 product of sine and cosine.
sin 6θ – sin 2θ
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Prove that:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
If secx cos5x + 1 = 0, where 0 < x ≤ `pi/2`, then find the value of x.
