NDA2022MathematicsTrigonometric Ratios & IdentitiesActual
What is the value of ^4 7 8 + ^4 5 8 ?
Options
- A3 2
- B3 4
- C3 8
- D3 16
Correct answer
B. 3 4
Step-by-step solution
aligned & ^4 7 8 + ^4 5 8 = ( ^2 7 8 )^2+ ( ^2 5 8 )^2 = & ( ^2 7 8 - ^2 5 8 )^2+2 ^2 7 8 ^2 5 8 = & [(-1) ( 7 8 + 5 8 ) ( 7 8 - 5 8 ) ]^2+ 1 2 [2 7 8 5 8 ]^2 = & [ 3 2 4 ]^2+ 1 2 [ 3 2 + 4 ]^2 aligned = [(-1) 1 2 ]^2+ 1 2 [0+ 1 2 ]^2= 1 2 + 1 4 = 3 4