Advertisements
Advertisements
प्रश्न
Prove that:
Advertisements
उत्तर
Consider LHS:
\[ \frac{\sin A + \sin 3A}{\cos A - \cos 3A}\]
\[ = \frac{2\sin \left( \frac{A + 3A}{2} \right) \cos \left( \frac{A - 3A}{2} \right)}{2\sin \left( \frac{A + 3A}{2} \right) \sin \left( \frac{3A - A}{2} \right)} \left\{ \because \sin A + \sin B = 2\sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right), and \cos A - \cos B = 2\sin \left( \frac{A + B}{2} \right) cos \left( \frac{B - A}{2} \right) \right\}\]
\[ = \frac{\sin 2A \cos \left( - A \right)}{\sin 2A \sin A}\]
\[ = \frac{\sin 2A \cos A}{\sin 2A \sin A}\]
\[ = \cot A\]
= RHS
Hence, LHS = RHS .
APPEARS IN
संबंधित प्रश्न
Prove that:
Prove that:
Show that :
Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]
Prove that:
tan 20° tan 40° tan 60° tan 80° = 3
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
If α + β = \[\frac{\pi}{2}\], show that the maximum value of cos α cos β is \[\frac{1}{2}\].
Express each of the following as the product of sines and cosines:
sin 12x + sin 4x
Express each of the following as the product of sines and cosines:
sin 5x − sin x
Prove that:
sin 23° + sin 37° = cos 7°
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
Prove that:
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 cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ
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 \[\frac{A - B}{2}\].
sin 163° cos 347° + sin 73° sin 167° =
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 80° = `1/8`
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:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
