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COMEDK2023MathematicsTrigonometric Ratios & Identities

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

Options

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

Correct answer

B. 2 A cosec A+2

Step-by-step solution

aligned & Given, 2 A 1- A + 2 A 1- A & = 2 A A 1- A A + 2 A A 1- A A & = ( A A ) ( 2 A A- A )+ ( A A ) ( 2 A A- A ) & = 2 A- A [ ^2 A A - ^2 A A ] & = 2 A- A [ ^3 A- ^3 A A A ] & = 2( A- A) ( 2 A+ ^2 A+ A A ) ( A- A)( A A) & =2 ( 1 A A +1 ) & =2( A cosec A+1)=2 A cosec A+2 aligned

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