AP EAMCET20225 Jul 2022Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual
In a triangle ABC , A 2 B 2 + B 2 C 2 + C 2 A 2 =
Options
- A0
- B1
- C1 2
Correct answer
B. 1
Step-by-step solution
A+B+C= aligned & A+B 2 = -C 2 & A 2 + B 2 = 2 - C 2 aligned aligned ( A 2 + B 2 ) & = ( 2 - C 2 ) & = C 2 ( i ) aligned Also, ( A 2 + B 2 )= A 2 + B 2 1- A 2 B 2 ...(ii) From (i) and (ii) C 2 = A 2 + B 2 1- A 2 B 2 1 c 2 = A 2 + B 2 1- A 2 B 2 1- A 2 B 2 = B 2 C 2 + C 2 A 2 A 2 B 2 + B 2 C 2 + C 2 A 2 =1