Advertisements
Advertisements
प्रश्न
Prove that:
उत्तर
Consider LHS:
\[ \frac{\cos A + cos B}{\cos B - \cos A}\]
\[ = \frac{2\cos \left( \frac{A - B}{2} \right) \cos \left( \frac{A + B}{2} \right)}{2\sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right)} \left[ \because \cos A + \cos B = 2\cos \left( \frac{A - B}{2} \right) \cos \left( \frac{A + B}{2} \right) and \cos A - \cos B = 2\sin \left( \frac{A + B}{2} \right) cos \left( \frac{B - A}{2} \right) \right]\]
\[ = \frac{\cos \left( \frac{A - B}{2} \right) \cos \left( \frac{A + B}{2} \right)}{\sin \left( \frac{A + B}{2} \right) sin \left( \frac{A - B}{2} \right)}\]
\[ = \cot\left( \frac{A + B}{2} \right)\cot\left( \frac{A - B}{2} \right)\]
=RHS
Hence, LHS = RHS.
APPEARS IN
संबंधित प्रश्न
Prove that:
Show that :
Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]
Show that:
sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0
Prove that
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]
Express each of the following as the product of sines and cosines:
sin 5x − sin x
Prove that:
sin 38° + sin 22° = sin 82°
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
sin 40° + sin 20° = cos 10°
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
\[\sin\frac{5\pi}{18} - \cos\frac{4\pi}{9} = \sqrt{3} \sin\frac{\pi}{9}\]
Prove that:
Prove that:
Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]
Prove that:
cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
If cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), then write the value of tan A tan B tan C.
cos 40° + cos 80° + cos 160° + cos 240° =
The value of cos 52° + cos 68° + cos 172° is
If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=
Express the following as the sum or difference of sine or cosine:
`sin "A"/8 sin (3"A")/8`
Express the following as the sum or difference of sine or cosine:
cos(60° + A) sin(120° + A)
Express the following as the sum or difference of sine or cosine:
`cos (7"A")/3 sin (5"A")/3`
Express the following as the product of sine and cosine.
sin 6θ – sin 2θ
Prove that:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`
