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The expression 2 A 1- A + 2 A 1- A can be written as

Options

  1. A2 A+ cosec 2 A
  2. B2 A+ 2 A
  3. C2 A+ 2 A
  4. D2 A cosec A+2

Correct answer

D. 2 A cosec A+2

Step-by-step solution

2 A 1 - A + 2 A 1 - A = 2 [ A A A - A A + A A A - A A ] = 2 [ ^2 A A( A - A) + ^2 A A( A - A) ] = 2 [ ^2 A A( A - A) - ^2 A A( A - A) ] = 2 [ ^3 A - ^3 A A A( A - A) ] = 2 [ ( A - A)( ^2 A + A A + ^2 A) A A( A - A) ] = 2 [ 1 + A A A A ] = 2 [ 1 A A + 1 ] = 2 A cosec A + 2

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