Advertisements
Advertisements
प्रश्न
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the values of cos(300°)
Find the values of `tan ((19pi)/3)`
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 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)
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 cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
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 A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a product
cos 65° + cos 15°
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
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 A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
