Advertisements
Advertisements
प्रश्न
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
उत्तर
cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
cos(30° + x) = cos 30°. cos x – sin 30° sin x
= `sqrt(3)/2 cos x - 1/2 sin x`
cos(30° + x) = `(sqrt(3)cosx- sinx)/2`
APPEARS IN
संबंधित प्रश्न
Find the values of tan(1050°)
Find the values of `tan ((19pi)/3)`
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
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)
Find the value of cos 105°.
Show that tan 75° + cot 75° = 4
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
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 θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
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 sum or difference
2 sin 10θ cos 2θ
Express the following as a product
cos 65° + cos 15°
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 `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
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
