English

In ∆ABC, if b2 + c2 − a2 = bc, then ∠A = ______. - Mathematics and Statistics

Advertisements
Advertisements

Question

In ∆ABC, if b2 + c2 − a2 = bc, then ∠A = ______.

Options

  • `pi/4`

  • `pi/3`

  • `pi/2`

  • `pi/6`

MCQ
Fill in the Blanks
Advertisements

Solution

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`

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.3: Trigonometric Functions - MCQ

RELATED QUESTIONS

In any ΔABC if  a2 , b2 , c2 are in arithmetic progression, then prove that Cot A, Cot B, Cot C are in arithmetic progression.


The principal solutions of cot x = -`sqrt3`  are .................


 In , ΔABC prove that 

`"sin"(("B" - "C")/2) = (("b" - "c")/"a") "cos"("A"/2)`                               


Find the Cartesian coordinates of the point whose polar coordinates are :

`(4,  pi/2)`


Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(1/2, (7pi)/3)`


Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(0, 1/2)`


Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(3/2, (3√3)/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:

ac cos B - bc cos A = a2 - b2


In any Δ ABC, prove the following:

`"cos 2A"/"a"^2 - "cos 2B"/"b"^2 = 1/"a"^2 - 1/"b"^2`


In Δ ABC, if ∠C = 90°, then prove that sin (A - B) = `("a"^2 - "b"^2)/("a"^2 + "b"^2)`


If `tan^-1 (("x" - 1)/("x" - 2)) + tan^-1 (("x" + 1)/("x" + 2)) = pi/4`, find the value of x.


Solve: `tan^-1 ("1 - x"/"1 + x") = 1/2 (tan^-1 "x")`, for x > 0.


In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______.


If polar co-ordinates of a point are `(3/4, (3pi)/4)`, then its Cartesian co-ordinate are ______


In ∆ABC, prove that ac cos B − bc cos A = a2 − b2 


With usual notations, prove that `(cos "A")/"a" + (cos "B")/"b" + (cos "C")/"c" = ("a"^2 + "b"^2 + "c"^2)/(2"abc")`


In ∆ABC, prove that `("b" - "c")^2 cos^2 ("A"/2) + ("b" + "c")^2 sin^2 ("A"/2)` = a2 


In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`


If the angles A, B, C of ΔABC are in A.P. and its sides a, b, c are in G.P., then show that a2, b2, c2 are in A.P.


In ∆ABC, prove that `(cos^2"A" - cos^2"B")/("a" + "b") + (cos^2"B" - cos^2"C")/("b" + "c") + (cos^2"C" - cos^2"A")/("c" + "a")` = 0


In ΔABC, prove that `("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")` = 0


In ΔABC, prove that `("b"^2 - "c"^2)/"a" cos"A" + ("c"^2 - "a"^2)/"b" cos"B" + ("a"^2 - "b"^2)/"c" cos "C"` = 0


In ∆ABC, if ∠A = `pi/2`, then prove that sin(B − C) = `("b"^2 - "c"^2)/("b"^2 + "c"^2)`


In ΔABC, if (a+ b - c)(a + b + c) = 3ab, then ______.


In a ΔABC, c2 sin 2B + b2 sin 2C = ?


With usual notations, if the angles A, B, C of a Δ ABC are in AP and b : c = `sqrt3 : sqrt2`.


If in a right-angled triangle ABC, the hypotenuse AB = p, then `overline"AB".overline" AC" + overline"BC".overline" BA" + overline" CA".overline"CB"` is equal to ______ 


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 one side of a triangle is double the other and the angles opposite to these sides differ by 60°, then the triangle is ______


The smallest angle of the ΔABC, when a = 7, b = `4sqrt(3)` and c = `sqrt(13)` is ______.


In a ΔABC, if a = `sqrt(2)` x and b = 2y and ∠C = 135°, then the area of triangle is ______.


In a ΔABC, if `("b" + "c")/11 = ("c" + "a")/12 = ("a" + "b")/13`, then cos C = ______.


In a triangle ABC, ∠C = 90°, then `(a^2 - b^2)/(a^2 + b^2)` is ______.


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 = ______.


In a triangle ABC, with usual notations, if \[\frac{2\cos\mathrm{A}}{\mathrm{a}}+\frac{\cos\mathrm{B}}{\mathrm{b}}+\frac{2\cos\mathrm{C}}{\mathrm{c}}=\frac{\mathrm{a}}{\mathrm{bc}}+\frac{\mathrm{b}}{\mathrm{ac}}\]then ∠A =


With usual notations, in a triangle ABC, if θ is any real number, then a cos(B - θ) + b cos (A + θ) is 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×