Question

I need help... please help me through this trigonometry. I need full answer.​

Answer 1

see explanation

Explanation:

Using the trigonometric identities

tan(x + y) =
`(tanx+tany)/(1-tanxtany)` , tan(x - y) =
`(tanx-tany)/(1+tanxtany)`, tan
`(\pi )/(4)` = 1

tan2x =
`(2tanx)/(1-tan^2x)`

Consider the left side

tan(
`(\pi )/(4)` + Θ ) - tan(
`(\pi )/(4)` - Θ )

=
`(tan(\pi )/(4)+tan0 )/(1-tan(\pi )/(4)tan0 )` -
`(tan(\pi )/(4)-tan0 )/(1+tan(\pi )/(4)tan0 )`

=
`(1+tan0)/(1-tan0)` -
`(1-tan0)/(1+tan0)`

=
`((1+tan0)^2-(1-tan0)^2)/((1-tan0)(1+tan0))`

=
`(1+2tan0+tan^20-1+2tan0-tan^20)/(1-tan^20)`

=
`(4tan0)/(1-tan^20)`

= 2
`(2tan0)/(1-tan^20)`

= 2 tan2Θ = right side