English

With Usual Notations, in δAbc, Prove that A(B Cos C − C Cos B) = B2 − C2

Advertisements
Advertisements

Question

With usual notations, in ΔABC, prove that a(b cos C − c cos B) = b2 − c2

Advertisements

Solution

L.H.S. = a(b cos C − c cos B)

= R.H.S.

 

shaalaa.com
  Is there an error in this question or solution?
2012-2013 (October)

APPEARS IN

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.


In a Δ ABC, with usual notations prove that:` (a -bcos C) /(b -a cos C )= cos B/ cos A`


In ΔABC, prove that `tan((A - B)/2) = (a - b)/(a + b)*cot  C/2`.


 

In ΔABC with usual notations, prove that 2a `{sin^2(C/2)+csin^2 (A/2)}` = (a +   c - b)

 

The angles of the ΔABC are in A.P. and b:c=`sqrt3:sqrt2` then find`angleA,angleB,angleC`

 


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

`(sqrt(2), pi/4)`


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

`(3/4, (3pi)/4)`


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.

`(sqrt(2), sqrt(2))`


In any Δ ABC, prove the following:

a2 sin (B - C) = (b2 - c2) sin A.


In Δ ABC, if a, b, c are in A.P., then show that cot `"A"/2, cot  "B"/2, cot  "C"/2` are also in A.P.


In Δ ABC, if sin2 A + sin2 B = sin2 C, then show that the triangle is a right-angled triangle.


With the usual notations, show that
(c2 − a2 + b2) tan A = (a2 − b2 + c2) tan B = (b2 − c2 + a2) tan C


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.`


Prove that `tan^-1 sqrt"x" = 1/2 cos^-1 ((1 - "x")/(1 + "x"))`, if x ∈ [0, 1]


Show that `(9pi)/8 - 9/4 sin^-1 (1/3) = 9/4 sin^-1 ((2sqrt2)/3)`.


If sin `(sin^-1  1/5 + cos^-1 x) = 1`, then find the value of x.


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


In ∆ABC, if cos A = `(sinB)/(2sinC)`, then ∆ABC is ______.


In ∆ABC, if sin2A + sin2B = sin2C, then show that a2 + b2 = c2 


In ΔABC, a = 3, b = 4 and sin A = `3/4`, find ∠B


In ∆ABC, if a = 13, b = 14, c = 15, then find the value of cos B


In ΔABC, if a cos A = b cos B, then prove that ΔABC is either a right angled or an isosceles triangle.


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


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 ________.


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, 2ab sin`((A + B - C)/2)` = ______


If `(- sqrt2, sqrt2)` are cartesian co-ordinates of the point, then its polar co-ordinates are ______.


In ΔABC if sin2A + sin2B = sin2C and l(AB) = 10, then the maximum value of the area of ΔABC is ______ 


If in a `triangle"ABC",` a2cos2 A - b2 - c2 = 0, then ______.


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


The number of solutions of the equation sin 2x – 2 cosx + 4 sinx = 4 in the interval [0, 5π] 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, 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 =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×