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:
Prove that:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]
Prove that:
tan 20° tan 40° tan 60° tan 80° = 3
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:
cos 12x + cos 8x
Prove that:
sin 38° + sin 22° = sin 82°
Prove that:
sin 50° − sin 70° + sin 10° = 0
Prove that:
cos 80° + cos 40° − cos 20° = 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:
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:
cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]
Prove that:
Prove that:
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 cos (A + B) sin (C − D) = cos (A − B) sin (C + D), prove that tan A tan B tan C + tan D = 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 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° =
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(60° + A) sin(120° + A)
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.
cos 2θ – cos θ
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
Evaluate-
cos 20° + cos 100° + cos 140°
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.
If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.
