If `sin4A-cos2A=cos4A-sin2A` `("where",0ltAlt(pi)/(4))`, then the value of tan 4A is

Options

A. 1
B. `(1)/(sqrt(3))`
C. `sqrt(3)`
D. `(sqrt(3)-1)/(sqrt(3)+1)`

Answer

C

Explanation

Given,
`sin44+sin2A=cos4A+cos2A`
`implies2sin3AcosA=2cos3AcosA`
`:." "sinx+siny`
`=2sin""((x+y)/(2))cos""((x-y)/(2))cosx+cosy`
`=2cos((x+y)/(2))cos((x-y)/(2))`
`:.tan3A=1" and "cosA=0`
`impliesA=(pi)/(12)" and "A=(pi)/(2)!in(0,(pi)/(4))`
`:." "tan4A=tan""(pi)/(3)=sqrt(3)`