1.

In ` A B C ,`if `A B=c`is fixed, and `cosA+cosB+2cos C=2`then the locus of vertex `C`isellipse (b) hyperbola (c)circle (d) parabola

Answer» `cosA+cosB+2cosC=2`
`cosA+cosB=2(1-cosC)`
`cosA+cosB=4sin^2(C/2)`
`2cos((A+B)/2)cos((A-B)/2)=4cis^2(C/2)`
`cos((A-B)/2)=2sinn(C/2)`
`2cos(C/2)cos((A-B)/2)=4sin(C/2)cos(C/2)`
`2sin((A+B)/2)cos((A-B)/2)=sinC`
`sinA+sinB=2sinC`
`a+b=2c`
Locus os vertex C isan ecllipse with vertex A and B as focii.


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