Answer:
D
Step-by-step explanation:
we can use the formula of tan(A-B) to solve this equation .
The formula is
[tex]tan(A-B)= \frac{tanA-tanB}{1+tanA.tanB}[/tex]
In our question , A is x and B is [tex]\frac{\pi }{3}[/tex]
so when we apply these in the question we get
[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-tan\frac{\pi }{3} }{1+tanx.tan\frac{\pi }{3} }[/tex]
Now since [tex]tan\frac{\pi }{3} = \sqrt{3}[/tex]
we get
[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-\sqrt{3} }{1+\sqrt{3} tanx.} }[/tex]
so correct option is
D
