AP EAMCET201824 Apr 2018Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
array r (1+ 8 ) (1+ 2 8 ) (1+ 3 8 ) (1+ 4 8 ) (1+ 5 8 ) (1+ 6 8 ) (1+ 7 8 )= array
Options
- A1 8
- B1 16
- C1 32
- D1 64
Correct answer
B. 1 16
Step-by-step solution
Given that, aligned & (1+ 8 ) (1+ 2 8 ) (1+ 3 8 ) & (1+ 4 8 ) (1+ 5 8 ) (1+ 6 8 ) (1+ 7 8 ) & = [1+ 8 ] [1+ 4 ] [1+ 3 8 ] [1+ 2 ] & [1+ ( - 3 8 ) ] [1+ 3 4 ] [1+ ( - 8 ) ] aligned aligned & = (1+ 8 ) (1+ 4 ) (1+ 3 8 ) & = (1+ 8 ) (1- 8 ) (1+ 3 8 ) (1+ 3 4 ) (1- 8 ) & = (1- ^2 8 ) (1- ^2 3 8 ) (1- 1 2 ) & = ^2 8 ^2 3 8 1 2 = 1 4 (2 ^2 8 ) (2 ^2 3 8 ) 1 2 & = 1 4 (1- 4 ) (1- 3 4 ) 1 2 & = 1 4 (1- 1 2 ) (1+ 1 2 ) 1 2 & = 1 4 (1- 1 2 ) 1 2 = 1 4 1 2 1 2 = 1 16 . aligned