Advertisements
Advertisements
प्रश्न
Prove that:
sin 38° + sin 22° = sin 82°
Advertisements
उत्तर
Consider LHS:
\[\sin 38^\circ + \sin 22^\circ\]
\[ = 2\sin \left( \frac{38^\circ + 22^\circ}{2} \right) \cos \left( \frac{38^\circ - 22^\circ}{2} \right) \left\{ \because \sin A + \sin B = 2\sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[ = 2\sin 30^\circ \cos 8^\circ\]
\[ = 2 \times \frac{1}{2}\cos(90^\circ - 8^\circ)\]
\[ = \sin 82^\circ\]
= RHS
Hence, LHS = RHS .
APPEARS IN
संबंधित प्रश्न
Prove that:
Show that :
Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that:
sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
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
Prove that:
sin 23° + sin 37° = cos 7°
Prove that:
sin 105° + cos 105° = cos 45°
Prove that:
sin 40° + sin 20° = cos 10°
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:
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A
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
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 \[m \sin\theta = n \sin\left( \theta + 2\alpha \right)\], prove that \[\tan\left( \theta + \alpha \right) \cot\alpha = \frac{m + n}{m - n}\]
If sin A + sin B = α and cos A + cos B = β, then write the value of tan \[\left( \frac{A + B}{2} \right)\].
The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.
cos 35° + cos 85° + cos 155° =
The value of sin 50° − sin 70° + sin 10° is equal to
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 x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =
If \[\tan\alpha = \frac{x}{x + 1}\] and
Express the following as the sum or difference of sine or cosine:
cos 7θ sin 3θ
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
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 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.
