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
Show that :
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]
Prove that tan 20° tan 30° tan 40° tan 80° = 1.
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
Prove that:
sin 38° + sin 22° = sin 82°
Prove that:
sin 23° + sin 37° = cos 7°
Prove that:
sin 105° + cos 105° = cos 45°
Prove that:
\[\sin\frac{5\pi}{18} - \cos\frac{4\pi}{9} = \sqrt{3} \sin\frac{\pi}{9}\]
Prove that:
Prove that:
cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), prove that tan A tan B tan C + tan D = 0.
If (cos α + cos β)2 + (sin α + sin β)2 = \[\lambda \cos^2 \left( \frac{\alpha - \beta}{2} \right)\], write the value of λ.
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° =
sin 163° cos 347° + sin 73° sin 167° =
sin 47° + sin 61° − sin 11° − sin 25° is equal to
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
Express the following as the product of sine and cosine.
sin 6θ – sin 2θ
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Prove that:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
Evaluate-
cos 20° + cos 100° + cos 140°
Evaluate:
sin 50° – sin 70° + sin 10°
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
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)]`
