Advertisements
Advertisements
Question
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
Advertisements
Solution
sin2 A – sin2 B = sin(A + B) sin(A – B)
L.H.S = sin2(A + B) – sin2(A – B)
= sin[(A + B) + (A – B)] [sin(A + B) – (A – B)]
= sin 2A sin 2B
= R.H.S
APPEARS IN
RELATED QUESTIONS
Find the values of cos(300°)
Find the values of tan(1050°)
Find the values of cot(660°)
Find the values of `sin (-(11pi)/3)`
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
Express the following as a sum or difference
2 sin 10θ cos 2θ
Show that sin 12° sin 48° sin 54° = `1/8`
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) =
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
