Advertisements
Advertisements
Question
Express each of the following as the product of sines and cosines:
sin 2x + cos 4x
Advertisements
Solution
\[\sin 2x + \cos 4x\]
\[ = \sin 2x + \sin \left( \frac{\pi}{2} - 4x \right)\]
\[ = 2\sin \left( \frac{2x + \frac{\pi}{2} - 4x}{2} \right) \cos \left( \frac{2x - \frac{\pi}{2} + 4x}{2} \right) \left\{ \because \sin A + \sin B = 2\sin\left( \frac{A + B}{2} \right)\cos\left( \frac{A - B}{2} \right) \right\}\]
\[ = 2\sin \left( \frac{\pi}{4} - x \right) \cos \left( 3x - \frac{\pi}{4} \right)\]
APPEARS IN
RELATED QUESTIONS
Prove that:
Prove that:
tan 20° tan 40° tan 60° tan 80° = 3
Prove that:
sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
Show that:
sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0
If α + β = \[\frac{\pi}{2}\], show that the maximum value of cos α cos β is \[\frac{1}{2}\].
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
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:
cos 55° + cos 65° + cos 175° = 0
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
If cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ
If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y − x) cot θ.
If A + B = \[\frac{\pi}{3}\] and cos A + cos B = 1, then find the value of cos \[\frac{A - B}{2}\].
cos 40° + cos 80° + cos 160° + cos 240° =
cos 35° + cos 85° + cos 155° =
If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=
If sin (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in
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(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.
cos 2A + cos 4A
Express the following as the product of sine and cosine.
cos 2θ – cos θ
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 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.
