Question

Question #72b1b

Answer 1

No Solutions(Ø)

Explanation:

`(1-tanx)^2=sec^2x-2secx`
`2secx-sec^2x+(1-tanx)^2=0`

We know that `tan^2x+1=sec^2x`,
Therefore,
`2secx-2tanx=0`
`secx-tanx=0`
`1/cosx-sinx/cosx=0`
`1/cosx(1-sinx)=0`
`therefore 1/cosx=0 or 1-sinx=0`

`-sinx=-1`(Assuming that `cosx≠0`)
`sinx=1`, `therefore x=2npi+pi/2(But cosx≠0)`
The roots `2npi+pi/2` doesn't satisfies `cosx≠0` for all `n∈ZZ`

Therefore `therefore`No Solutions`(x∈Ø)`