`(1 + sec 2 theta)(1 + sec 2^(2) theta)(1 + sec 2^(3)` is equal is

Options

A. `cot 8 theta tan theta`
B. `tan 4theta cot theta`
C. `tan 8theta cot theta`
D. none of these

Answer

3

Explanation

`((1 + cos 2 theta)/(cos 2 theta))((1+ cos 4 theta)/(cos 4theta))((1+ cos 8 theta)/(cos 8 theta))`
`= (2cos^(2) theta)/(cos 2 theta)(2 cos^(2) 2theta)/(cos 2 theta)(2cos^(2)4theta)/(cos8 theta)`
`=(cos theta cos 2theta(sin 4theta)(2cos^(2) 4 theta))/(sin theta cos 2 theta cos2^(2)theta cos 8 theta)`
`=(cos theta cos 2 theta(sin 4 theta)(2 cos^(2) 4 theta))/(sin theta cos 2theta cos 2^(2) thetacos 8 theta)`
`=(cos theta cos 2theta cos 4theta cos 8 theta)/(sin theta cos 2theta cos2^(2) theta cos 8theta)`
`=tan 8 theta cot theta`