`f(x)=sin^2x+cos^4x+2` and `g(x)=cos(cosx)+cos(sinx)` Also let period f(x) and g(x) be `T_1` and `T_2` respectively then

Options

A. `T_(1)=2T_(2)`
B. `2T_(1)=T_(2)`
C. `T_(1)=T_(2)`
D. `T_(1)=4T_(2)`

Answer

C

Explanation

`f(x)=sin^(2)x+(1-sin^(2)x)^(2)+2`
`=3-sin^(2)x+sin^(4)x`
`=3-sin^(2)xcos^(2)x`
`=3-(sin^(2)2x)/(4)`
`rArr" "T_(1)=(pi)/(2), and T_(2)=(pi)/(2)`