AP EAMCET2005MathematicsTrigonometric Equations
If 2 x=( 2 +1) ( x- 1 2 ), x 1 2 , then x
Options
- A2 n 3 : n Z
- B2 n 6 : n Z
- C2 n 2 : n Z
- D2 n 4 : n Z
Correct answer
D. 2 n 4 : n Z
Step-by-step solution
aligned & 2 x=( 2 +1) ( x- 1 2 ) & 2 x= 2 x-1+ x- 1 2 & 1+ 2 x= x( 2 +1)- 1 2 & 2 ^2 x- x( 2 +1)+ 1 2 =0 & x= ( 2 +1) ( 2 +1)^2- 8 2 2(2) & = ( 2 +1) 3+2 2 -4 2 4 & = ( 2 +1) ( 2 -1)^2 4 & = 2 +1 ( 2 -1) 4 & aligned on taking + ve sign aligned x & = 2 +1+ 2 -1 4 = 2 2 4 = 1 2 x & =2 n 4 n Z aligned