Question

Math: https://snipboard.io/gYGE5n.jpg
The options: https://snipboard.io/OyZVls.jpg

Answer 1

\[\tan \left( x+\theta \right)=\frac{ tanx +\tan \theta }{ 1-tanxtan \theta}\]
and
\[\theta=\frac{ k \pi }{ 4 }\]
where
k is an integer
You must must kook which value of k will give the correct answer

Answer 2

Hmmmmm so how to I find out what number k will be? Like how do I start?

Answer 3

\[\tan \left( \frac{ \pi }{ 4}+x \right)=\frac{ \tan \frac{ \pi }{ 4 }+\tan x }{ \tan \frac{ \pi }{ 4}-\tan x} =\frac{ 1+\tan x }{1- \tan x } \]
\[\tan x=\tan (x+n \pi)\]
where n is an integer.
\[\tan (\frac{ \pi }{ 4 }+x)=\tan (n \pi+\frac{ \pi }{ 4 }+x)\]
where n is an integer.
n=...-2,-1,0,1,2,...
when n=-2,we get \[\tan (-2\pi+\frac{ \pi }{ 4 }+x)=\tan (-\frac{ 7 \pi}{ 4 }+x)\]
so D is the solution.

Answer 4

Hmmmm interesting I see so it would be tan (x - (7π/4))

Answer 5

yes

Answer 6

Omg ty this makes so much sense!