Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\text{ LHS }= \sin\frac{x}{2}\sin\frac{7x}{2} + \sin\frac{3x}{2}\sin\frac{11x}{2}\]
\[ = \frac{1}{2}\left[ 2\sin\frac{x}{2}\sin\frac{7x}{2} + 2\sin\frac{3x}{2}\sin\frac{11x}{2} \right]\]
\[ = \frac{1}{2}\left[ \cos\left( \frac{7x}{2} - \frac{x}{2} \right) - \cos\left( \frac{7x}{2} + \frac{x}{2} \right) + \cos\left( \frac{11x}{2} - \frac{3x}{2} \right) - \cos\left( \frac{11x}{2} + \frac{3x}{2} \right) \right]\]
\[ = \frac{1}{2}\left[ \cos3x - \cos4x + \cos4x - \cos7x \right]\]
\[ = \frac{1}{2}\left[ \cos3x - \cos7x \right]\]
\[ = \frac{1}{2}\left[ - 2\sin\left( \frac{3x + 7x}{2} \right)\sin\left( \frac{3x - 7x}{2} \right) \right]\]
\[ = \frac{1}{2}\left[ - 2\sin\left( 5x \right)\sin\left( - 2x \right) \right]\]
\[ = \sin\left( 5x \right)\sin\left( 2x \right) =\text{ RHS }\]
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
tan 20° tan 40° tan 60° tan 80° = 3
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:
sin 12x + sin 4x
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
sin 50° + sin 10° = cos 20°
Prove that:
sin 23° + sin 37° = cos 7°
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
Prove that:
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A
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:
Prove that:
If \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
If A + B = \[\frac{\pi}{3}\] and cos A + cos B = 1, then find the value of cos \[\frac{A - B}{2}\].
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
sin 163° cos 347° + sin 73° sin 167° =
The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.
cos 35° + cos 85° + cos 155° =
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
If \[\tan\alpha = \frac{x}{x + 1}\] and
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 (7"A")/3 sin (5"A")/3`
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.
cos 2θ – cos θ
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
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.
