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 sin(480°)
Find the values of sin (– 1110°)
Find the values of tan(1050°)
Find the values of `sin (-(11pi)/3)`
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)
Find the value of cos 105°.
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin 105° + cos 105° = cos 45°
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
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)`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
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 sum or difference
sin 35° cos 28°
Express the following as a sum or difference
sin 5θ sin 4θ
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
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
