in triangle abc, angle c=120degress
cos square a + cos square b + cosa.cosb=?

Question

in triangle abc, angle c=120degress
cos square a + cos square b + cosa.cosb=?

shubhamsrg · Answer

Is there any other info given ? About the triangle or anything ?

anonymous · Answer

no... angle c is 120 degree and we need tofind find $$\cos ^{2}a+\cos ^{2}b+cosa.cosb$$
options are: a)3/4   b) 3/2   c)   1/2   d)  1/4

shubhamsrg · Answer

@ganeshie8

anonymous · Answer

wat happened

shubhamsrg · Answer

I am unable to solve this. But I tagged @ganeshie8 . He'll probably be able to help you.

anonymous · Answer

okay thank you

shubhamsrg · Answer

Nah, I don't think that is correct. a=b=30 degrees does not yield any of the options.

anonymous · Answer

the quesiotn and options both are correct....a=b=30 is not necessary... take a+b=60 and try to split th multiplication xpressions into additive expressions... eg. 2cos((C+D)/2)cos((C-D)/2)=cos(C+D)+cos(C-D)

anonymous · Answer

im not able to get it

ganeshie8 · Answer

try below :

A+B = 60
c^2 = a^2 + b^2 + 1

cos^2A + cos^2B + cosAcosB =  (cosA + cosB)^2 - cosAcosB

ganeshie8 · Answer

I think @shubhamsrg is right, the options are incorrect as a=b=30 does not yield any of  the options

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=evaluate+cos%5E2A+%2B+cos%5E2B+%2B+cosA*cosB%2C+C+%3D+2pi%2F3%2C+A+%3D+pi%2F6%2C+B+%3D+pi%2F6