The number of solutions of the equation `cos6x+tan^2x+cos(6x)tan^2x=1` in the interval `[0,2pi]` is (a)`4` (b)` 5` (c) `6` (d) `7`

Explanation

`cos6x+tan^2x+cos6x*tan^2x=1`

`cos6x[1+tan^2x]=1-tan^2x`

`cos6x=(1-tan^2x)/(1+tan^2x)`

`cos6x=cos2x`

`cos6x-cos2x=0`

`-2sin((6x+2x)/2)*sin((6x-2x)/2)=0`

`-2sin4xsin2x=0`

`sin4x=0`

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