Advertisements
Advertisements
प्रश्न
Express the following as a sum or difference
cos 5θ cos 2θ
Advertisements
उत्तर
cos 5θ cos 2θ
We know
cosA cosB = `1/2`[cos(A + B) + cos(A – B)]
Take A = 5θ, B = 2θ
cos 5θ . cos 2θ = `1/2`[cos(5θ + 2θ) + cos(5θ – 2θ)]
cos 5θ . cos 2θ = `1/2`[cos 7θ + cos 3θ]
APPEARS IN
संबंधित प्रश्न
Find the values of cot(660°)
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
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 sin(A + B)
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 sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Express the following as a product
cos 35° – cos 75°
Show that `cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
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`
