Advertisements
Advertisements
Question
Advertisements
Solution
\[\text{ LHS }= \cos x \cos\frac{x}{2} - \cos 3x \cos\frac{9x}{2}\]
\[ = \frac{1}{2}\left[ 2\cos x \cos\frac{x}{2} - 2\cos 3x \cos\frac{9x}{2} \right]\]
\[ = \frac{1}{2}\left[ \cos\left( x + \frac{x}{2} \right) + \cos\left( x - \frac{x}{2} \right) - \cos\left( 3x + \frac{9x}{2} \right) - \cos\left( 3x - \frac{9x}{2} \right) \right]\]
\[ = \frac{1}{2}\left[ \cos\frac{3x}{2} + \cos\frac{x}{2} - \cos\frac{15x}{2} - \cos\frac{3x}{2} \right]\]
\[ = \frac{1}{2}\left[ \cos\frac{x}{2} - \cos\frac{15x}{2} \right]\]
\[ = \frac{1}{2}\left[ - 2\sin\left( \frac{x + 15x}{4} \right)\sin\left( \frac{x - 15x}{4} \right) \right]\]
\[ = \frac{1}{2}\left[ - 2\sin\left( 4x \right)\sin\left( - \frac{7x}{2} \right) \right]\]
\[ = \sin\left( 4x \right)\sin\left( \frac{7x}{2} \right) = \text{ RHS }\]
Hence, LHS = RHS
Notes
Disclaimer: The given question is incorrect. The correct question should be
APPEARS IN
RELATED QUESTIONS
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:
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 12x + sin 4x
Express each of the following as the product of sines and cosines:
sin 5x − sin x
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
sin 105° + cos 105° = cos 45°
Prove that:
sin 40° + sin 20° = cos 10°
Prove that:
\[\sin\frac{5\pi}{18} - \cos\frac{4\pi}{9} = \sqrt{3} \sin\frac{\pi}{9}\]
Prove that:
Prove that:
Prove that:
Prove that:
cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]
Prove that:
Prove that:
Prove that:
Prove that:
If cosec A + sec A = cosec B + sec B, prove that tan A tan B = \[\cot\frac{A + B}{2}\].
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 \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), then write the value of tan A tan B tan C.
If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=
The value of sin 50° − sin 70° + sin 10° is equal to
sin 47° + sin 61° − sin 11° − sin 25° 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 2θ – cos θ
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Prove that:
2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0
Evaluate:
sin 50° – sin 70° + sin 10°
If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.
