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If =k then ( + 2 ) is equal to

Options

  1. Ak+1 k-1 ( - 2 )
  2. Bk-1 k+1 ( - 2 )
  3. Ck+1 k-1 ( - 2 )
  4. Dk-1 k+1 ( - 2 )

Correct answer

C. k+1 k-1 ( - 2 )

Step-by-step solution

Given = k , we have = k . Applying componendo and dividendo: + - = k+1 k-1 Using the sum-to-product formulas A + B = 2 ( A+B 2 ) ( A-B 2 ) and A - B = -2 ( A+B 2 ) ( A-B 2 ) : 2 ( + 2 ) ( - 2 ) -2 ( + 2 ) ( - 2 ) = k+1 k-1 - ( + 2 ) ( - 2 ) = k+1 k-1 ( + 2 ) = - k+1 k-1 1 ( - 2 ) ( + 2 ) = k+1 1-k ( - 2 ) Since ( - 2 ) = - ( - 2 ) , we have: ( + 2 ) = k+1 k-1 ( - 2 ) Answer: k+1 k-1 ( - 2 )

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