Home
Class 12
MATHS
If a,b and A are given in a triangle and...

If a,b and A are given in a triangle and `C_(1), C_(2)` are the possible values of the third side, prove that : `C_(1)^(2)+C_(2)^(2)-2C_(1) C_(2) cos 2A=4a^(2)cos ^(2)A`

Text Solution

Verified by Experts

The correct Answer is:
5
Promotional Banner

Similar Questions

Explore conceptually related problems

If a, b and A are given in a triangle and c_(1), c_(2) are possible values of the third side, then prove that c_(1)^(2) + c_(2)^(2) - 2c_(1) c_(2) cos 2A = 4a^(2) cos^(2)A

For any triangle ABC, prove that : (b^(2)-c^(2))cotA+(c^(2)-a^(2))cotB+(a^(2)-b^(2))cotC=0 .

If g, h, k denotes the side of a pedal triangle, then prove that (g)/(a^(2))+ (h)/(b^(2))+ (k)/(c^(2))=(a^(2)+b^(2) +c^(2))/(2 abc)

If A+B+C=pi , prove that : cot (A/2)+ cot(B/2) + cot(C/2) = cot(A/2) cot (B/2) cot (C/2)

If A,B,C are the angles of a triangle then prove that cosA+cosB-cosC=-1+4cos(A/2)cos(B/2)sin(C/2)

For any triangle ABC, prove that : (b+c)cos((B+C)/(2))=acos((B-C)/(2))

For DeltaABC prove that, (a-b)^(2)cos^(2)""(C)/(2)+(a+b)^(2)sin^(2)""(C)/(2)=c^(2)

For any triangle ABC, prove that : sin""(B-C)/(2)=(b-c)/(a)cos((A)/(2))

If a,b,and c are the side of a triangle and A,B and C are the angles opposite to a,b,and c respectively, then Delta=|{:(a^(2),bsinA,CsinA),(bsinA,1,cosA),(CsinA,cos A,1):}| is independent of

For any triangle ABC, prove that : a(cosC-cosB)=2(b-c)cos^(2)""(A)/(2)