Advertisements
Advertisements
प्रश्न
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
पर्याय
30°
60°
75°
45°
Advertisements
उत्तर
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to 75°.
Explanation:
`angle"B"` = 60° `angle"A"` + `angle"C"` = 120
Now,
`b/c = sqrt3/sqrt2 = sin B/sin A`
sin C = `1/sqrt2`
`angle"C"` = 45°
Hence, `angle"A"` = 75°
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
cosθ + sinθ = 1.
State whether the following equation have solution or not?
3 tanθ = 5
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
If `sqrt3`cos x - sin x = 1, then general value of x is ______.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin θ - cos θ = 1
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
If | x | < 1, then prove that
`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Find the principal solutions of cosec x = 2
Find the principal solutions of cos 2𝑥 = 1
Find the principal solutions of tan x = `-sqrt(3)`
`cos^-1 (cos (4pi)/3)` = ______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
The general solution of sec θ = `sqrt2` is
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The principal solutions of cot x = `sqrt3` are ______.
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
The general solution of the equation tan θ tan 2θ = 1 is given by ______
Which of the following is true in a triangle ABC?
If sin θ + cos θ = 1, then the general value of θ is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The general solution of cosec x = `-sqrt2` is ______
Find the principal solutions of cot θ = 0
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
The number of principal solutions of tan 2θ = 1 is ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
