Advertisements
Advertisements
प्रश्न
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Advertisements
उत्तर
L.H.S = sin(A + B) sin(A – B)
= (sin A cos B + cos A sin B) (sin A cos B – cos A sin B)
= sin2A cos2B – cos2A sin2B
= sin2A(1 – sin2B) – (1 – sin2A) sin2B
= sin2A – sin2A sin2B – sin2B + sin2A sin2B
= sin2A – sin2B
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of tan(1050°)
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
If sin A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(A – B)
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin 75° – sin 15° = cos 105° + cos 15°
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a product
cos 65° + cos 15°
Show that sin 12° sin 48° sin 54° = `1/8`
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
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
