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Manipal MET2021MathematicsTrigonometric Equations

If A- A+a=0, A is equal to

Options

  1. Aa^2-1 a^2+1
  2. B1-a^2 1+a^2
  3. Ca^2+1 a^2-1
  4. D1+a^2 1-a^2

Correct answer

B. 1-a^2 1+a^2

Step-by-step solution

Given, A- A=-a aligned & 1- A A =-a & 1- A 1- ^2 A =-a & 1+ ^2 A-2 A=a^2 (1- ^2 A ) & (1+a^2 ) ^2 A-2 A+ (1-a^2 )=0 & ( A-1) [ A- (1-a^2 ) (1+a^2 ) ]=0 & A=1 or A= 1-a^2 1+a^2 aligned

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