A function `f(theta)=sin^(2)theta+3sin theta cos theta+5cos^(2)theta` is defined `AA theta in R`. Another function`g(theta)=f((pi)/(2)-theta)` at the point `theta` where `f(theta)` is minimum, then thevalue of `(1)/(g(theta))` is

Options

A. 2
B. 5
C. 3
D. 4

Answer

A

Explanation

`f(theta)=sin^(2)theta+3 sin theta cos theta cos theta + 5 cos^(2) theta`
`=1+4 cos^(2) theta + (3)/(2) sin 2 theta`
`3+2 cos 2theta + (3)/(2) sin 2 theta`
Minimum of `f(theta)` and `f((pi)/(2)-theta)` will be same because of the type of function a `sin theta+b cos theta` and is `3-(5)/(2)=(1)/(2)`
`therefore g(theta)=(1)/(2)`
`therefore (1)/(g(theta))=2`