Advertisements
Advertisements
प्रश्न
Express each of the following as the product of sines and cosines:
sin 2x + cos 4x
Advertisements
उत्तर
\[\sin 2x + \cos 4x\]
\[ = \sin 2x + \sin \left( \frac{\pi}{2} - 4x \right)\]
\[ = 2\sin \left( \frac{2x + \frac{\pi}{2} - 4x}{2} \right) \cos \left( \frac{2x - \frac{\pi}{2} + 4x}{2} \right) \left\{ \because \sin A + \sin B = 2\sin\left( \frac{A + B}{2} \right)\cos\left( \frac{A - B}{2} \right) \right\}\]
\[ = 2\sin \left( \frac{\pi}{4} - x \right) \cos \left( 3x - \frac{\pi}{4} \right)\]
APPEARS IN
संबंधित प्रश्न
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
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:
cos 12x + cos 8x
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
Prove that:
sin 47° + cos 77° = cos 17°
Prove that:
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A
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:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y − x) cot θ.
If \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos2 (θ − ϕ) =
cos 35° + cos 85° + cos 155° =
If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=
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.
sin A + sin 2A
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
Evaluate:
sin 50° – sin 70° + sin 10°
If sin(y + z – x), sin(z + x – y), sin(x + y – z) are in A.P, then prove that tan x, tan y and tan z are in A.P.
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
