A general solution of `tan^(2) theta+ cos 2 theta=1` is `(n in Z)`

Options

A. `n pi-pi/4`
B. `2npi+pi/4`
C. `npi+pi/4`
D. `n pi`

Answer

A, C, D

Explanation

We have
`tan^(2) theta=1-cos 2 theta=2 sin^(2) theta` or `cosec^(2) theta tan^(2) theta=2`
or `(1+cot^(2) theta) tan^(2) theta=2` or `tan^(2) theta+1=2`
or `tan^(2) theta=1`
or `tan theta = pm 1`
`rArr theta=n pi pm pi/4, n in Z`
Moreover, `tan^(2) theta=2 sin^(2) theta`
`rArr sin^(2) theta=0rArr theta = npi`