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
- A2
- B3
- C4
- 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)