Advertisements
Advertisements
प्रश्न
Express each of the following as the product of sines and cosines:
sin 12x + sin 4x
Advertisements
उत्तर
\[\sin 12x + sin 4x\]
\[ = 2\sin \left( \frac{12x + 4x}{2} \right) \cos\left( \frac{12x - 4x}{2} \right) \left\{ \because \sin A + \sin B = 2\sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[ = 2 \sin 8x \cos 4x\]
APPEARS IN
संबंधित प्रश्न
Prove that:
Prove that:
Prove that:
Prove that tan 20° tan 30° tan 40° tan 80° = 1.
Express each of the following as the product of sines and cosines:
cos 12x + cos 8x
Prove that:
sin 50° + sin 10° = cos 20°
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
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:
Prove that:
cos (A + B + C) + cos (A − B + C) + cos (A + B − C) + cos (− A + B + C) = 4 cos A cos Bcos C
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
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
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° =
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
cos 35° + cos 85° + cos 155° =
The value of sin 50° − sin 70° + sin 10° is equal to
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =
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 A + sin 2A
Evaluate-
cos 20° + cos 100° + cos 140°
If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
