SOLUTION: (1+cosA)(1+cosB)(1+ cosC) = (1-cosA)(1-cosB)(1-cosC) Show that one of the values of each member of this equality is sin A sinB sinC.

Algebra ->  Trigonometry-basics -> SOLUTION: (1+cosA)(1+cosB)(1+ cosC) = (1-cosA)(1-cosB)(1-cosC) Show that one of the values of each member of this equality is sin A sinB sinC.      Log On


   



Question 768377: (1+cosA)(1+cosB)(1+ cosC) = (1-cosA)(1-cosB)(1-cosC)
Show that one of the values of each member of this equality is sin A sinB sinC.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(1+cosA)(1+cosB)(1+ cosC) = (1-cosA)(1-cos(B)(1-cos(C))
member of this equality is sin A sinB sinC.
-----------------------
[(1+cosA)(1+cosB)(1+ cosC)]/[(1-cosA)(1-cosB)(1-cosC)]
------
Multiply numerator and denominator by [(1+cosA)(1+cosB)(1+ cosC]
to get::
[(1+cosA)(1+cosB)(1+ cosC)]^2 /[sin^2(a)(sin^2(B)(sin^2(C)
-------------------
etc.
=====
Cheers,
Sta H.
==============