If `tan^2theta=2tan^2phi+1`, then which one of the following is correct?

Options

A. `cos(2theta=cos(2phi)-1`
B. `cos(2theta)=cos(2phi)+1`
C. `cos(2theta)=[cos(2phi)-1]//2`
D. `cos(2theta)=[cos(2phi)+1]//2`

Answer

C

Explanation

Work with option , `cos(2phi)-1=(1-tan^(2)phi)/(1+tan^(2)phi)-1`
`=-(2tan^(2)phi)/(1+tan^(2)phi)=(-(tan^(2)theta-1))/(1+(tan^(2)theta-1)/(2))`
`=(1-tan^(2)theta)/(1+tan^(2)theta)xx2=cos(2theta)2`
Thus , `cos2theta=(cos(2phi)-1)/(2)`