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 all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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 cos(x − y)
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
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)`
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Express the following as a sum or difference
cos 5θ cos 2θ
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
