Advertisements
Advertisements
प्रश्न
Prove that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
Advertisements
उत्तर
Consider LHS:
\[\sin (B - C) \cos (A - D) + \sin (C - A) \cos (B - D) + \sin (A - B) \cos (C - D)\]
Multiplying by 2:
\[ 2\sin (B - C) \cos (A - D) + 2\sin(C - A) \cos (B - D) + 2\sin (A - B) \cos (C - D)\]
\[ = \sin \left( B - C + A - D \right) + \sin \left( B - C - A + D \right) + \sin \left( C - A + B - D \right) + \sin \left( C - A - B + D \right) + \sin \left( A - B + C - D \right) + \sin \left( A - B - C + D \right)\]
\[ = \sin\left\{ - \left( C + D - A - B \right) \right\} + \sin\left\{ - \left( A + C - B - D \right) \right\} + \sin\left\{ - \left( A + D - B - C \right) \right\} + \sin\left( C - A - B + D \right) + \sin\left( A - B + C - D \right) + \sin\left( A - B - C + D \right)\]
\[ = - \sin\left( C + D - A - B \right) - \sin\left( A + C - B - D \right) - \sin\left( A + D - B - C \right) + \sin\left( C - A - B + D \right) + \sin\left( A - B + C - D \right) + \sin\left( A - B - C + D \right)\]
\[ = 0\]
= RHS
Hence, LHS = RHS.
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 tan 20° tan 30° tan 40° tan 80° = 1.
Prove that
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]
Express each of the following as the product of sines and cosines:
cos 12x + cos 8x
Prove that:
sin 50° + sin 10° = cos 20°
Prove that:
sin 23° + sin 37° = cos 7°
Prove that:
Prove that:
Prove that:
Prove that:
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 cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ
If sin A + sin B = α and cos A + cos B = β, then write the value of tan \[\left( \frac{A + B}{2} \right)\].
Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]
The value of cos 52° + cos 68° + cos 172° is
cos 35° + cos 85° + cos 155° =
sin 47° + sin 61° − sin 11° − sin 25° is equal to
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 product of sine and cosine.
sin 6θ – sin 2θ
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
