Advertisements
Advertisements
Question
Express the following as a sum or difference
sin 5θ sin 4θ
Solution
sin 5θ sin 4θ
We know
sin A sin B = `1/2`[cos(A – B) – cos(A + B)]
Take A = 5θ, B = 4θ
sin 5θ . sin 4θ = `1/2`[cos(5θ – 4θ) – cos(5θ + 4θ)]
sin 5θ . sin 4θ = `1/2`[cos θ – cos 9θ]
APPEARS IN
RELATED QUESTIONS
Find the values of tan(1050°)
Find the values of `tan ((19pi)/3)`
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 x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Find the value of cos 105°.
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a product
cos 35° – cos 75°
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
