Advertisements
Advertisements
प्रश्न
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Advertisements
उत्तर
cos θ = `1/2 ("a" + 1/"a")`
cos 3θ = 4 cos3θ – 3 cos θ
= `4[1/2("a" + 1/"a")]^3 - 3[1/2("a" + 1/"a")]`
= `4 xx 1/8("a" + 1/"a")^3 - 3/2("a" + 1/"a")`
= `1/2("a" + 1/"a")^3 - 3/2("a" + 1/"a")`
= `1/2["a"^3 + 3"a"^2(1/"a") + 3"a"(1/"a")^2 + 1/"a"^3] - 3/2(a" + 1/"a")`
= `1/2["a"^3 + 3"a" + 3/"a" + 1/"a"^3] - 3/2"a" - 3/(2"a")`
= `1/2 "a"^3 + 3/2"a" + 3/(2"a") + 1/(2"a"^3) - 3/2"a" - 3/(2"a")`
cos 3θ = `1/2"a"^3 + 1/(2"a"^3)`
= `1/2("a"^3 + 1/"a"^3)`
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the values of cos(300°)
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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 a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Express the following as a product
sin 75° sin 35°
Show that sin 12° sin 48° sin 54° = `1/8`
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
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`
