Advertisements
Advertisements
प्रश्न
Express each of the following as the product of sines and cosines:
cos 12x - cos 4x
Advertisements
उत्तर
\[\cos 12x - \cos 4x\]
\[ = - 2\sin \left( \frac{12x + 4x}{2} \right) \sin \left( \frac{12x - 4x}{2} \right) \left\{ \because \cos A - \cos B = - 2\sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right) \right\}\]
\[ = - 2 \sin 8x \sin 4x\]
APPEARS IN
संबंधित प्रश्न
Prove that:
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]
Prove that:
sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
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 50° + sin 10° = cos 20°
Prove that:
Prove that:
Prove that:
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
If cosec A + sec A = cosec B + sec B, prove that tan A tan B = \[\cot\frac{A + B}{2}\].
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
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
cos 40° + cos 80° + cos 160° + cos 240° =
The value of sin 50° − sin 70° + sin 10° is equal to
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
Express the following as the sum or difference of sine or cosine:
cos 7θ sin 3θ
Express the following as the product of sine and cosine.
sin A + sin 2A
Express the following as the product of sine and cosine.
cos 2A + cos 4A
Express the following as the product of sine and cosine.
cos 2θ – cos θ
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
Prove that:
2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.
