If A + B + C = 180(degree) Show that
cosA + cosB + cosC = 1 + 4 sinA/2 sinB/2 sinC/2
2007-02-22 22:36:10 · 3 answers · asked by Hermione 2 in Science & Mathematics ➔ Mathematics
Pl.refer to any book on Trigonometry in Mathematics which gives the solution for this problem
2007-02-27 04:08:33 · answer #1 · answered by balakrishnan c 3 · 0⤊ 0⤋
I haven't worked through the whole thing, but I'm sure that it involves converting the whole angles on the LHS to half angles using an adaption of the double angle formula. You might also have to use the first condition to replace one angle by 180 - other two angles. That should be enough to get you started. Try to do it yourself before looking at anyone's detailed answer left here.
2007-02-23 07:01:12 · answer #2 · answered by mathsmanretired 7 · 0⤊ 0⤋
cosA+cosB = 2cosA+B/2.cosA-B/2
2cosA+B/2.cosA-B/2+cosC
2cos(90-C/2)cosA-B/2=1-2sin*C/2 [*refers to square.]
2sinC/2(cosA-B/2-sinC/2)+1
2sinC/2(cosA-B/2-cosA+B/2)+1
Try expanding the one in the bracket.Then you will get....
2sinC/2(2sinA/2.sinB/2)+1
=1+4sinA/2.sinB/2.sinC/2
2007-02-23 06:49:30 · answer #3 · answered by ♦Opty misstix♦ 7 · 1⤊ 0⤋