NDA2021MathematicsTrigonometric Ratios & IdentitiesActual
Let A B C be a triangle. If 2 A+ 2 B+ 2 C=-1 then which one of the following is correct?
Options
- AA B C=0
- BA B C=0
- CA B C=0
- DA B C=0
Correct answer
D. A B C=0
Step-by-step solution
aligned & A+B+C= & C= -(A+B) & Now, 2 A+ 2 B+ 2 C=-1 & 2 (A+B) (A-B)+2 ^2 C-1=-1 & 2 (A+B) (A-B)+2 ^2( -(A+B))=0 & 2 (A+B)[ (A-B)+ (A+B)]=0 & 2 ( -C)[2 A B]=0 & -4 C A B=0 & A B C=0 aligned