Trig. Law of Cosines

Show that any triangle with standard labeling...
a^2+b^2+c^2/2abc = cos(alpha)/a + cos(beta)/b + cos(gamma)/c

I don't get it. Can someone please help me.

Start here with the law of cosines:
a^2 = b^2 + c^2 -2bc Cos A
b^2 = a^2 + c^2 -2ac Cos B
c^2 = a^2 + b^2 - 2ab Cos C

Add the three equations. divide both sides by 2abc

  1. 👍 0
  2. 👎 0
  3. 👁 211

Respond to this Question

First Name

Your Response

Similar Questions

  1. trig

    Given sin a = 15/17 with a in Quadrant I and cos beta = 4/5 with beta in QuandrantIV, find the exact value of cos(a+beta)

  2. math

    if cos(B-C)+cos(C-A)+cos(A-B)=-3/2 then prove that cosA+cosB+cosC=O and sinA+sinB+sinC=O after that prove that cos(B-C)=cos(C-A)=cos(A-B)=-1/2

  3. Math

    Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx I did some of these so far, don't know if it is correct. Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx

  4. self-study calculus

    Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t)=cos(t)I -cos(t)j+sin(t)k I don't know what to do. I let x=cos(t), y=-cos(t) and z= sin(t). Should I let t be any

  1. maths

    prove that the length of the perpendicular from the origin to the straight line joining the two points having coordinates ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is a cos { ( alpha + beta)/2}.

  2. Pre-Cal (Trig) Help?

    The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. So I'm pretty

  3. Trigonometry

    Three oil platforms, Alpha, Beta and Gamma are situated in the North Sea.Beta is 12 km from Alpha and is on a bearing of 145 degrees from Alpha.Gamma is 16 km from Alpha and is on a bearing of 220 degrees from Alpha.Find the

  4. Physics

    Equation b=a square ×cos square×2π×beta×Gama÷alpha . The unit of a, alpha, beta are metre , 1/ sec and m/sec. Respectively the unit of b and gamma are

  1. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

  2. Calculus

    Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help. Calculus - Steve, Tuesday, January 12, 2016 at

  3. Maths

    Cos^4(θ)/cos^2(α) + sin^4(θ)/ sin^2(α)=1 Prove that cos^4 alpha/cos^ thetha + sin^4alpha/ sin^2thetha= 1

  4. math

    Find the values of sin θ, cos θ, and tan θ for the given right triangle (in the link below). Give the exact values. sin θ= cos θ= tan θ= my answer is c^2 = a^2 +b^2 c^2 = 5^2+12^2 c^2 =

You can view more similar questions or ask a new question.