Advertisements
Advertisements
प्रश्न
The value of sin 50° − sin 70° + sin 10° is equal to
विकल्प
1
0
`1/2`
2
Advertisements
उत्तर
0
\[\sin50^\circ - \sin70^\circ + \sin10^\circ\]
\[ = 2\sin\left( \frac{50^\circ - 70^\circ}{2} \right) \cos\left( \frac{50^\circ + 70^\circ}{2} \right) + \sin10^\circ \left[ \because \sin A - \sin B = 2\sin\left( \frac{A - B}{2} \right)\cos\left( \frac{A + B}{2} \right) \right]\]
\[ = 2\sin\left( - 10^\circ \right) \cos60^\circ + \sin10^\circ\]
\[ = 2 \times \frac{1}{2}\sin\left( - 10^\circ \right) + \sin10^\circ\]
\[ = - \sin10^\circ + \sin10^\circ\]
\[ = 0\]
APPEARS IN
संबंधित प्रश्न
Prove 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 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
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 4x
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
cos 20° + cos 100° + cos 140° = 0
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:
sin 47° + cos 77° = cos 17°
Prove that:
cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
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 \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
cos 40° + cos 80° + cos 160° + cos 240° =
sin 163° cos 347° + sin 73° sin 167° =
If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos2 (θ − ϕ) =
The value of cos 52° + cos 68° + cos 172° is
sin 47° + sin 61° − sin 11° − sin 25° is equal to
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
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:
2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0
Evaluate-
cos 20° + cos 100° + cos 140°
