Need this for a presentation please help
ABCDE is inscribed in a circle with AB=BC=CD=DE=4 and AE=1. Compute
(1-cosB)(1-cosACE)
1 Answer
As suggested by Kav10, you need to use Cosine law for triangles ABC and ACE, and that that AC=CE.
Using Cosine law on the trianles ABC we have
\[AC^2=AB^2+BC^2-2AB \cdot BC \cos B=4^2+4^2-2\cdot 4\cdot 4 \cos B.\]
Hence
\[AC^2=32(1-\cos B). (1)\]
Using Cosine law on the trianles ACE we have
\[AE^2=AC^2+CE^2-2AC \cdot CE\cos (ACE),\]
since $AC=CE$ we get
\[1^2=AC^2+AC^2-2AC^2 \cos (ACE)=2AC^2(1-\cos (ACE)),\]
or
\[\frac{1}{2AC^2}=(1-\cos (ACE)). (2)\]
Multiplying (1) and (2) we get
\[\frac{1}{2}=32(1-\cos B)(1-\cos (ACE)).\]
Hence
\[(1-\cos B)(1-\cos (ACE))=\frac{1}{64}\]

4.8K
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- 1 Answer
- 380 views
- Pro Bono
Related Questions
- Solve the equation $x^4-5x^2+6=0$
- How to show that the composition of two riemannian isometries is an isometry?
- Determine formula to calculate the radii of a unique ellipsoid from coordinates of non-coplanar locii on its surface, and without knowing its center or rotation angles.
- Help deriving an equation from geometry and vectors
- Analyzing Concave Down Segments of the Sinusoidal Curve
- Petra is organising a team building activity day with work colleagues . She is considering two options, which both offer packages for groups of up...
- I need help on this problem! it's trigonometric functions I believe. If you could show your work that would be even better! Thank you guys
- Calculate the angle of an isosceles triangle to cover a distance on a plane
Use the Cosine Theorem for triangles ABC and ACE. Note that AC=CE. If you want full solution, it deserves a bounty.