Advertisements
Advertisements
प्रश्न
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
Advertisements
उत्तर
sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\]
\[= \frac{1}{2} \times 2\left( \sin\frac{\pi}{12} \right) \left( \sin\frac{5\pi}{12} \right)\]
\[ = \frac{1}{2}\left[ \cos\left( \frac{\pi}{12} - \frac{5\pi}{12} \right) - \cos\left( \frac{\pi}{12} + \frac{5\pi}{12} \right) \right] \left[ \because 2\sin A \sin B = \cos(A - B) - \cos(A + B) \right]\]
\[ = \frac{1}{2}\left[ \cos\left( - \frac{\pi}{3} \right) - \cos\frac{\pi}{2} \right]\]
\[ = \frac{1}{2}\left( \frac{1}{2} - 0 \right)\]
\[ = \frac{1}{4}\]
APPEARS IN
संबंधित प्रश्न
Prove 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:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
Prove that:
sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
Prove that:
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]
If α + β = \[\frac{\pi}{2}\], show that the maximum value of cos α cos β is \[\frac{1}{2}\].
Prove that:
sin 23° + sin 37° = cos 7°
Prove that:
Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]
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 \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
If sin A + sin B = α and cos A + cos B = β, then write the value of tan \[\left( \frac{A + B}{2} \right)\].
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
sin 163° cos 347° + sin 73° sin 167° =
The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.
If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =
If \[\tan\alpha = \frac{x}{x + 1}\] and
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
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`
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
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 secx cos5x + 1 = 0, where 0 < x ≤ `pi/2`, then find the value of x.
