The expression `(tan^4x+2tan^2x+1)cos^2x ,w h e nx=pi/(12),` can be equal to `4(2-sqrt(3))` (b) `4(sqrt(2)+1)` `16cos^2pi/(12)` (d) `16sin^2pi/(12)`

Options

A. `4(2-sqrt(3))`
B. `4(sqrt(2)+1)`
C. `16cos^(2)pi//12`
D. `16sin^(2)pi//12`

Answer

A, D

Explanation

`=y=((1+tan^(2)x)^(2))/(1+tan^(2)x)=1+tan^(2)x`
`=1+(2-sqrt(3))^(2)`
`=8-4sqrt(3)=4(2-sqrt(3))`
`=4[(sqrt((3)/(2))-(1)/sqrt(2))^(2)]`
`4[4((sqrt(3)-1)/(2sqrt(2)))^(2)]`
`=16sin^(2)((pi)/(12))`