Number of roots of the equation `2^(tan(x-pi/4))-2(0. 25)^sin^(3((x-pi/4))/(cos2x))+1=0,i s_______`

Answer

0

Explanation

`(sin^(2) (x-pi/4))/(cos 2x)=(1/2 (sin x-cos x)^(2))/(cos^(2) x-sin^(2) x)`
`=(-1/2 (sin x - cos x))/(cos x + sin x)=-1/2 tan (x-pi/4)`
Given equation reduces to
`2^(tan(x-pi/4)-2(0.25)^(-1/2 tan(x-pi/4))+1=0`
`rArr 2^(tan(x-pi/4)=1`
`rArr x=pi//4`, which is not possible as `cos 2x=0` for this value for `x`, which is not defining the original equation.