Advertisements
Advertisements
प्रश्न
In ∆ABC, if b2 + c2 − a2 = bc, then ∠A = ______.
विकल्प
`pi/4`
`pi/3`
`pi/2`
`pi/6`
Advertisements
उत्तर
In ∆ABC, if b2 + c2 − a2 = bc, then ∠A = `bbunderline(pi/3)`.
Explanation:
By cosine rule,
`cos A = (b^2 + c^2 - a^2)/(2 bc)`
∴ `cos A = (bc)/(2 bc)` ...[b2 + c2 − a2 = bc]
∴ `cos A = 1/2`
∴ `angle A = pi/3`
APPEARS IN
संबंधित प्रश्न
In a Δ ABC, with usual notations prove that:` (a -bcos C) /(b -a cos C )= cos B/ cos A`
In Δ ABC, if a = 13, b = 14 and c = 15, then sin (A/2)= _______.
(A) `1/5`
(B) `sqrt(1/5)`
(C) `4/5`
(D) `2/5`
The angles of the ΔABC are in A.P. and b:c=`sqrt3:sqrt2` then find`angleA,angleB,angleC`
If in ∆ABC with usual notations a = 18, b = 24, c = 30 then sin A/2 is equal to
(A) `1/sqrt5`
(B) `1/sqrt10`
(C) `1/sqrt15`
(D) `1/(2sqrt5)`
Find the Cartesian co-ordinates of the point whose polar co-ordinates are:
`(sqrt(2), pi/4)`
Find the Cartesian coordinates of the point whose polar coordinates are :
`(4, pi/2)`
Find the polar co-ordinates of the point whose Cartesian co-ordinates are.
`(sqrt(2), sqrt(2))`
Find the polar co-ordinates of the point whose Cartesian co-ordinates are.
`(0, 1/2)`
In any Δ ABC, prove the following:
a sin A - b sin B = c sin (A - B)
In any ΔABC, prove the following:
`("c" - "b cos A")/("b" - "c cos A") = ("cos B")/("cos C")`
In any Δ ABC, prove the following:
a2 sin (B - C) = (b2 - c2) sin A.
In any Δ ABC, prove the following:
`("b" - "c")/"a" = (tan "B"/2 - tan "C"/2)/(tan "B"/2 +tan "C"/2)`
In ΔABC, if `"cos A"/"a" = "cos B"/"b"`, then show that it is an isosceles triangle.
Show that `2 sin^-1 (3/5) = tan^-1(24/7)`
Show that
`tan^-1(1/5) + tan^-1(1/7) + tan^-1(1/3) + tan^-1 (1/8) = pi/4.`
If `tan^-1 (("x" - 1)/("x" - 2)) + tan^-1 (("x" + 1)/("x" + 2)) = pi/4`, find the value of x.
In ∆ABC, if cos A = `(sinB)/(2sinC)`, then ∆ABC is ______.
If polar co-ordinates of a point are `(3/4, (3pi)/4)`, then its Cartesian co-ordinate are ______
In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`
In ΔABC, prove that `("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")` = 0
In a ΔABC, c2 sin 2B + b2 sin 2C = ?
In a triangle ABC, If `(sin "A" - sin "C")/(cos "C" - cos "A")` = cot B, then A, B, C are in ________.
In Δ ABC; with usual notations, if cos A = `(sin "B")/(sin "C")`, then the triangle is _______.
In a ΔABC, `(sin "C"/2)/(cos(("A" - "B")/2))` = ______
In a ΔABC, 2ab sin`((A + B - C)/2)` = ______
If `(- sqrt2, sqrt2)` are cartesian co-ordinates of the point, then its polar co-ordinates are ______.
If P(6, 10, 10), Q(1, 0, -5), R(6, -10, λ) are vertices of a triangle right angled at Q, then value of λ is ______.
In Δ ABC, with the usual notations, if `(tan "A"/2)(tan "B"/2) = 3/4` then a + b = ______.
In ΔABC if sin2A + sin2B = sin2C and l(AB) = 10, then the maximum value of the area of ΔABC is ______
In ΔABC, if `cosA/a = cosB/b,` then triangle ABC is ______
If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle is ______.
If in a `triangle"ABC",` a2cos2 A - b2 - c2 = 0, then ______.
In ΔABC, `cos"A"/"a" = cos"B"/"b" cos"C"/"c"`. If a = `1/sqrt(6)`, then the area of the triangle is ______.
If in a triangle ABC, AB = 5 units, AB = 5 units, ∠B = `cos^-1 (3/5)` and radius of circumcircle of ΔABC is 5 units, then the area (in sq.units) of ΔABC is ______.
If in a ΔABC `a cos^2(C/2) + c cos^2(A/2) = (3b)/2`, then the sides a, b and c ______.
In a triangle ABC, ∠C = 90°, then `(a^2 - b^2)/(a^2 + b^2)` is ______.
In ΔABC, `(a - b)^2 cos^2 C/2 + (a + b)^2 sin^2 C/2` is equal to ______.
In any ΔABC, prove that:
(b + c) cos A + (c + a) cos B + (a + b) cos C = a + b + c.
If in ΔABC, `sin A/2 * sin C/2 = sin B/2` and 2s is the perimeter of the triangle, then s = ______.
The perimeter of ΔABC is 20, ∠A = 60°, area of ΔABC = `10sqrt(3)`, then find the values of a, b, c.
In ΔABC, a = 3, b = 1, cos(A – B) = `2/9`, find c.
If the angles A, B, C of a ΔABC are in A.P. and ∠A = 30°, c = 5, then find the values of ‘a’ and ‘b’.
