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AP EAMCET20226 Jul 2022Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The value of ^4 x is

Options

  1. A3 8 + 1 2 2 x+ 1 8 4 x
  2. B3 8 - 1 2 2 x+ 1 8 4 x
  3. C3 8 - 1 8 4 x+ 1 2 2 x
  4. D1 8 4 x+ 1 2 2 x- 3 8

Correct answer

A. 3 8 + 1 2 2 x+ 1 8 4 x

Step-by-step solution

Given expression is ^4 x . aligned & 2 x=2 ^2 x-1 & ^2 x= 1+ 2 x 2 aligned Take, ^4 x = ( ^2 x )^2= ( 1+ 2 x 2 )^2 aligned & = 1+ ^2 2 x+2 2 x 4 & = 1 4 + ( 1+ 4 x 2 ) 1 4 + x 2 & = 1 4 + 1 8 + 4 x 8 + 2 x 2 & = 3 8 + 1 2 2 x+ 1 8 4 x aligned

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