NDA2016MathematicsTrigonometric Ratios & IdentitiesActual
What is the value of (1+ 8 ) (1+ 3 8 ) (1+ 5 8 ) (1+ 7 8 ) ?
Options
- A1 2
- B1 2 + 1 2 2
- C1 2 - 1 2 2
- D1 8
Correct answer
D. 1 8
Step-by-step solution
[1+ 8 ] [1+ 3 8 ] [1+ 5 8 ] [1+ 7 8 ] We have, aligned & 7 8 = [ - 8 ]=- 8 & and 5 8 = [ - 3 8 ]=- 3 8 & = [1+ 8 ] [1+ 3 8 ] [1- 8 ] [1- 3 8 ] & = [1- ^2 8 ] [1- ^2 3 8 ]= ^2 8 ^2 3 8 & = 1 4 [2 ^2 8 2 ^2 3 8 ] & = 1 4 [ (1- 4 ) (1- 3 4 ) ] & = 1 4 [ (1- 1 2 ) (1+ 1 2 ) ]= 1 8 aligned