AP EAMCET202319 May 2023Morning ShiftMathematicsTrigonometric EquationsActual
If A+ B+ C=0= A+ B+ C , then (A-B)=
Options
- A0
- B1 2
- C- 2 3
- D- 1 2
Correct answer
D. - 1 2
Step-by-step solution
Given A+ B+ C=0= A+ B+ C ...(i) Now A+ B+ C=0 aligned & 2 ( A-B 2 ) ( A+B 2 )+ C=0 & 2 ( A-B 2 ) ( A+B 2 )=- C aligned ( A-B 2 )= - C 2 ( A+B 2 ) ...(ii) Again now A+ B+ C=0 (given) 2 ( A+B 2 ) ( A-B 2 )+ C=0 ( A-B 2 )=- C 2 ( A+B 2 ) ...(iii) From (ii) and (iii), we have aligned & - C 2 ( A+B 2 ) =- C 2 ( A+B 2 ) & C= ( A+B 2 ) & C = A+B 2 aligned putting C = A+B 2 in equation (ii), we get ( A-B 2 )= - ( A+B 2 ) 2 ( A+B 2 ) ( A-B 2 )=- 1 2 we know that aligned & (A-B)=2 ^2 ( A-B 2 )-1 & =2 (- 1 2 )^2-1=- 1 2 align