AP EAMCET202316 May 2023Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual
If ^3 x 4 x = _ r =0 ^ n a _ r rx x R , then a₃+a₅: a₁+a₇=
Options
- A1: 3
- B1: 1
- C2: 1
- D3: 1
Correct answer
D. 3: 1
Step-by-step solution
^3 x 4 x= 1 2 (2 4 x x) ^2 x aligned & = 1 2 [ 5 x+ 3 x] ^2 x & = 1 4 [ 6 x+2 4 x+ 2 x] x & = 1 8 [ 7 x+3 5 x+3 3 x+ x] & =a₁ x+a₂ 2 x+a₃ 3 x+ . & a₁= 1 8 , a₃= 3 8 , a₅= 3 8 , a₇= 1 8 aligned Now, a₃+a₅: a₁+a₇=3: 1