MHT CET20239 May 2023Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual
If 2 B- (A+C) (A-C) , Then A, B, C are in
Options
- AGeometric Progression.
- BArithmetic Progression.
- CHarmonic Progression.
- DArithmetico-Geometric Progression.
Correct answer
A. Geometric Progression.
Step-by-step solution
aligned & 2 B= (A+C) (A-C) & 1- ^2 B 1+ ^2 B = A C- A C A C+ A C & 1- ^2 B 1+ ^2 B = A C(1- A C) A C(1+ A C) & 1- ^2 B 1+ ^2 B = (1- A C) (1+ A C) aligned aligned & (1- ^2 ~B )(1+ A C ) & =(1- A C ) (1+ ^2 ~B ) & 1+ A C - ^2 ~B - ^2 ~B A C & =1+ ^2 ~B - A C - A C ^2 ~B & 2 A C =2 ^2 ~B & ^2 ~B = A C & A , B , C are in G.P. aligned