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AP EAMCET202527 May 2025Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A and B are acute angles satisfying 3 ^2 A+2 ^2 B=4 and 3 A B = 2 B A , then A+2 B=

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

A. 2

Step-by-step solution

We have, array rlrl & 3 ^2 A+2 ^2 B=4 & 3 (1- ^2 A )+2 (1- ^2 B ) & =4 & 5-3 ^2 A-2 ^2 B & =4 & 3 ^2 A+2 ^2 B & =1 & & 3 ^2 A & =1-2 ^2 B & & 3 ^2 A & = 2 B array Again, aligned & 3 A B = 2 B A & 3 A A=2 B B & 3 2 A=2 2 B & = A 2 B- A 2 B & = A (3 ^2 A )- A ( 3 2 2 A ) & =3 A ^2 A-3 ^2 A A=0 & A+2 B=90^ & aligned Now, (A+2 B)

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