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COMEDK2021MathematicsTrigonometric Ratios & Identities

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

Options

  1. AA A+1
  2. BA cosec A+1
  3. CA+ A
  4. DA+ cosec A

Correct answer

B. A cosec A+1

Step-by-step solution

Let the expression be E = A 1- A + A 1- A . Substituting A = 1 A into the expression: E = A 1- 1 A + 1 A 1- A E = ^2 A A - 1 + 1 A(1- A) E = ^2 A A - 1 - 1 A( A - 1) E = ^3 A - 1 A( A - 1) Using the identity a^3 - b^3 = (a-b)(a^2 + ab + b^2) where a = A and b = 1 : E = ( A - 1)( ^2 A + A + 1) A( A - 1) E = ^2 A + A + 1 A E = A + 1 + A E = 1 + A A + A A E = 1 + ^2 A + ^2 A A A E = 1 + 1 A A E = 1 + A cosec A . Answer: A cosec A+1

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