Home
Class 11
MATHS
112. If in a Delta ABC, cosA+ cosB + cos...

112. If in a `Delta ABC, cosA+ cosB + cosc =3/2.` Prove that `DeltaABC` is an equilateral triangle.

Text Solution

Verified by Experts

`cosA+cosB+cosC=3/2`
`2(2cos((A+B)/2)cos((A-B)/2))+2cosC=3`
`2(2cos((pi-C)/2) cos((A-B)/2))+2cosC=3`
`4cos(pi/2-C/2)cos((A-B)/2)+2cosC=3`
`4sin(C/2)cos((A-B)/2)+2(1-2sin^2C/2)=3`
`4sin^2(C/2)-4sin(C/2)cos((A-B)/2)+1=0-(1)`
`D>=0`
`b^2-4ac>=0`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

In DeltaABC if (cosA)/a=(cosB)/b=(cosC)/c Prove that DeltaAB C is equilateral.

In DeltaABC if (cosA)/a=(cosB)/b=(cosC)/c Prove that DeltaAB C is equilateral.

For a DeltaABc, it is given that cosA +cosB+cosC=3/2. prove that the Delta is equilateral.

If in triangle ABC cosA+cosB+cosC=3/2 then prove that triangle is equilateral

In any triangle ABC, if cosA + cos B + cosC =3/2 , then show that the triangle is equilateral.

In /_\ABC ,a/cosA=b/cosB=c/cosC.Show that the triangle is equilateral.

If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the triangle are in AP

If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the triangle are in AP

If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the triangle are in AP

In a triangle ABC, (cosB+cosC)/(1-cosA) =