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MHT CET202522 Apr 2025Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A=n (A+2 B) , then (A+B)=

Options

  1. A1+n 2-n B
  2. B1-n 1+n B
  3. C1-n 2+n B
  4. D1+n 1-n B

Correct answer

D. 1+n 1-n B

Step-by-step solution

Given A = n (A+2B) , rewrite the angles using compound angle formulas. Expressing in terms of A+B and B : A = ((A+B)-B) = (A+B) B - (A+B) B (A+2B) = ((A+B)+B) = (A+B) B + (A+B) B Substitute into the original equation: (A+B) B - (A+B) B = n( (A+B) B + (A+B) B) Rearrange terms to isolate factors: (A+B) B(1 - n) = (A+B) B(1 + n) Divide both sides by (A+B) B : (A+B)(1 - n) = B(1 + n) Solving for (A+B) yields: (A+B) = 1+n 1-n B Final answer: D

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