Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\text{ LHS }= \cos x \cos\frac{x}{2} - \cos 3x \cos\frac{9x}{2}\]
\[ = \frac{1}{2}\left[ 2\cos x \cos\frac{x}{2} - 2\cos 3x \cos\frac{9x}{2} \right]\]
\[ = \frac{1}{2}\left[ \cos\left( x + \frac{x}{2} \right) + \cos\left( x - \frac{x}{2} \right) - \cos\left( 3x + \frac{9x}{2} \right) - \cos\left( 3x - \frac{9x}{2} \right) \right]\]
\[ = \frac{1}{2}\left[ \cos\frac{3x}{2} + \cos\frac{x}{2} - \cos\frac{15x}{2} - \cos\frac{3x}{2} \right]\]
\[ = \frac{1}{2}\left[ \cos\frac{x}{2} - \cos\frac{15x}{2} \right]\]
\[ = \frac{1}{2}\left[ - 2\sin\left( \frac{x + 15x}{4} \right)\sin\left( \frac{x - 15x}{4} \right) \right]\]
\[ = \frac{1}{2}\left[ - 2\sin\left( 4x \right)\sin\left( - \frac{7x}{2} \right) \right]\]
\[ = \sin\left( 4x \right)\sin\left( \frac{7x}{2} \right) = \text{ RHS }\]
Hence, LHS = RHS
Notes
Disclaimer: The given question is incorrect. The correct question should be
APPEARS IN
संबंधित प्रश्न
Prove that:
Show that :
Show that :
Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]
Prove that:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]
Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]
Prove that:
sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
Express each of the following as the product of sines and cosines:
cos 12x + cos 8x
Express each of the following as the product of sines and cosines:
cos 12x - cos 4x
Prove that:
sin 50° + sin 10° = cos 20°
Prove that:
cos 20° + cos 100° + cos 140° = 0
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:
If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y − x) cot θ.
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
sin 47° + sin 61° − sin 11° − sin 25° is equal to
If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=
If \[\tan\alpha = \frac{x}{x + 1}\] and
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 2A + cos 4A
Express the following as the product of sine and cosine.
sin 6θ – sin 2θ
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
Find the value of tan22°30′. `["Hint:" "Let" θ = 45°, "use" tan theta/2 = (sin theta/2)/(cos theta/2) = (2sin theta/2 cos theta/2)/(2cos^2 theta/2) = sintheta/(1 + costheta)]`
