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

Explanation

`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`

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