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MHT CET202123 Sep 2021Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If in A A B C , with usual notations, a^2, b^2, c^2 are in A.P. then 3 B B =

Options

  1. Aa^2-c^2 2 a c
  2. B( a^2-c^2 2 a c )^2
  3. Ca ^2- c ^2 ac
  4. D( a^2-c^2 a c )^2

Correct answer

B. ( a^2-c^2 2 a c )^2

Step-by-step solution

We have 2 b^2=a^2+c^2 aligned & 3 ~B B = 3 B -4 ^2 ~B B & =3-4 ^2 ~B =3-4 (1- ^2 ~B )=4 ^2 ~B -1 & =4 [ c ^2+ a ^2- b ^2 2 ac ]^2-1=4 [ b ^2 2 ac ]-1 & = ( 2 ~b ^2 2 ac )-1= ( a ^2+ c ^2 2 ac )-1= ( a ^2+ c ^2 2 ac +1 ) ( a ^2+ c ^2 2 ac -1 ) & = ( a + c )^2( a - c )^2 (2 ac )^2 & = [ ( a + c )( a - c ) 2 ac ]= ( a ^2- c ^2 2 ac )^2 aligned

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