Advertisements
Advertisements
प्रश्न
Show that :
Advertisements
उत्तर
\[LHS = 2\sin25^\circ \cos 115^\circ\]
\[ = \frac{\sin \left( 25^\circ + 115^\circ \right) + \sin \left( 25^\circ - 115^\circ \right)}{2} \left[ \because \sin A \cos B = \frac{1}{2}\left\{ \sin (A + B) + \sin (A - B) \right\} \right]\]
\[ = \frac{\sin 140^\circ + \sin \left( - 90^\circ \right)}{2}\]
\[ = \frac{\sin 140^\circ - \sin \left( 90^\circ \right)}{2}\]
\[ = \frac{\sin 140^\circ - 1}{2} \]
\[RHS = \frac{\sin 140^\circ - 1}{2}\]
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
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:
sin 2x + cos 4x
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
Prove that:
Prove that:
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]
Prove that:
cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]
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 \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
If 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 sin 78° − sin 66° − sin 42° + sin 60° is ______.
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 (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in
Express the following as the sum or difference of sine or cosine:
`sin "A"/8 sin (3"A")/8`
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 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:
tan 20° tan 40° tan 80° = `sqrt3`.
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:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
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.
