Advertisements
Advertisements
Question
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Advertisements
Solution
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
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
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 cos(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 sin(π + θ) = − sin θ.
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
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`
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a product
cos 35° – cos 75°
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) =
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
