Advertisements
Advertisements
Question
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Solution
L.H.S = cos 8θ cos 2θ
= cos(5θ + 3θ) cos(5θ – 3θ)
We know cos(A + B) cos(A – B)
= cos2 A – sin2 B
∴ cos(5θ + 3θ) cos(5θ – 3θ) = cos25θ – sin23θ
= R.H.S
APPEARS IN
RELATED QUESTIONS
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
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 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 tan(x + y)
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 cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
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 4x cos 2x
Express the following as a sum or difference
sin 5θ sin 4θ
Express the following as a product
cos 35° – cos 75°
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
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:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
