Question

三角形ABC中，a、b、c分别是A、B、C的对边，且有sin2C+根号3*cos(A+B)=0(1)若a=4,c=根号13，求三角形ABC的

三角形ABC中，a、b、c分别是A、B、C的对边，且有sin2C+根号3*cos(A+B)=0(1)若a=4,c=根号13，求三角形ABC的面积

Answer 1

sin2C+√3cos(A+B)=0
sin2C+√3cos(pi-C)=0
2sinCcosC-√3cosC=0
cosC(sinC-(√3)/2)=0
所以:cosC=0, 或sinC=(√3)/2
而:a=4,c=√13
a>c 如cosC=0，则C=90度，A<C, a<c,与条件矛盾,所以cosC=0不成立
所以:sinC=(√3)/2, C=pi/3
a/sinA=c/sinC
sinA=(a/c)sinC=(2/13)√39
cosA=(1-(12/13))^(1/2)=（√13）/13
sinB=sin(pi-(A+C))=sin(A+C)=sinAcosC+cosAsinC
=(3/26)√39
△ABC的面积=(1/2)ac*sinB=3√3

Answer 2

a(3a-2b)=3(c+b)(c-b)，
变形得（a²+b²-c²）/2ab=1/3
就是cosC=1/3
则sinC=2√2/3
sin2C+cos（2A+2B)
=sin2C+cos2C
=2sinCcosC+cos²C-sin²C
=（4√2-7）/9

Answer 3

A wonderful Federer to try out five wins and why low,ghd ceramic hair straightener

Federer

Perhaps nobody might have thought Federer this Wimbledon will be the Big 4 is the initial out of that one. Wimbledon men's singles quarter-finals today of a war, Federer leading two great scenario to be reversed Songane, after a year ago missed the semi-finals once once more.

soon show up on the conference website. "Always lose a bit bit unacceptable,ceramic hair straightener, but today he played an almost ideal game. Get the very first set after the break, like I no longer get any break points. I also involve some opportunities,chi hair products, but the key moment of his usually in a position to try out some good shots. "Federer stated these days actually play to their own great," Absolutely nothing wrong, except the score, I was with my performance today was satisfied, even though I out a bit uncomfortable, but this really is tennis. a minimum of he played such a high level was able to get over me using this sense,InStyler Hair Crimping Iron, really feel a little better. "" He and I've played prior to, I understand he can play great time what kind of ball, however the third set that he broke my serve a bit unusual, let me break a way tough to accept. then he may be very potent serve, few opportunities personally.

"fifth set was separated on Federer is not a bit discouraged? "This is not a issue, the issue is each and every time he saw my small chance to serve when he boldly offensive, and work every time, he believed himself in this critical moment that truly hit the winning objective, which You've to give him lots of praise. "" competition process rapidly, and suddenly I was in the final set within the behind,the hair straightener, the scenario looks extremely poor, but in fact you really feel fairly great. This is a bit unfortunate. "