Question

The equation tan(x- pi/3) is equal to _____.

Answer 1

Answer:

B

Step-by-step explanation:

Using the expansion

tan(x - y) = $\frac{tanx-tany}{1+tanxtany}$, then

tan(x - $\frac{\pi }{3}$)

=  $\frac{tanx-tan(-\frac{\pi }{3}) }{1+tanxtan(-\frac{\pi }{3}) }$

note that tan( -$\frac{\pi }{3}$) = - tan($\frac{\pi }{3}$) = - $\sqrt{3}$

= $\frac{tanx-(-\sqrt{3}) }{1+tanx(-\sqrt{3}) }$

= $\frac{tanx+\sqrt{3} }{1-\sqrt{3}tanx }$ → B

Answer 2

Answer:

D

Step-by-step explanation:

we can use the formula of tan(A-B) to solve this equation .

The formula is

$tan(A-B)= \frac{tanA-tanB}{1+tanA.tanB}$

In our question , A is x and B is $\frac{\pi }{3}$

so when we apply these in the question we get

$tan(x-\frac{\pi }{3} )=\frac{tanx-tan\frac{\pi }{3} }{1+tanx.tan\frac{\pi }{3} }$

Now since $tan\frac{\pi }{3} = \sqrt{3}$

we get

$tan(x-\frac{\pi }{3} )=\frac{tanx-\sqrt{3} }{1+\sqrt{3} tanx.} }$

so correct option is

D