Advertisements
Advertisements
प्रश्न
Express the following as the sum or difference of sine or cosine:
`sin "A"/8 sin (3"A")/8`
Advertisements
उत्तर
`sin "A"/8 sin (3"A")/8 = 1/2(2 sin "A"/8 sin (3"A")/8)`
[∵ 2 sin A sin B = cos(A – B) – cos(A + B)
`= 1/2[cos ("A"/8 - (3"A")/8) - cos("A"/8 + (3"A")/8)]`
`= 1/2 [cos (("A" - 3"A")/8) - cos (("A" + 3"A")/8)]`
`= 1/2 [cos ((- 2"A")/8) - cos ("4A"/8)]`
`= 1/2 [cos ((- "A")/4) - cos ("A"/2)]`
`= 1/2 [cos "A"/4 - cos "A"/2]` ...[∵ cos(-θ) = cos θ]
APPEARS IN
संबंधित प्रश्न
Express each of the following as the product of sines and cosines:
sin 12x + sin 4x
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 105° + cos 105° = cos 45°
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 cos (A + B) sin (C − D) = cos (A − B) sin (C + D), prove that tan A tan B tan C + tan D = 0.
Find the value of tan22°30′. `["Hint:" "Let" θ = 45°, "use" tan theta/2 = (sin theta/2)/(cos theta/2) = (2sin theta/2 cos theta/2)/(2cos^2 theta/2) = sintheta/(1 + costheta)]`
