Advertisements
Advertisements
Question
Express the following as the sum or difference of sine or cosine:
`sin "A"/8 sin (3"A")/8`
Advertisements
Solution
`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
RELATED QUESTIONS
Prove that:
Prove that:
Prove that:
sin 47° + cos 77° = cos 17°
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
Write the value of \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]
Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
