Question

The value of the expression \(tan(x-9π)\) is equal to:

• A. \(-tanx\)
• B. \(-cotx\)
• C. \(tanx\)
• D. \(cotx\)

Hint:

The tangent has period $\pi$, so subtracting $9\pi$ changes nothing.

Answer 1

The Correct Option is C

Step 1: Reduce step by step
Each shift of $\pi$ returns tangent to its own value, because $\tan(x-\pi)=\frac{\sin(x-\pi)}{\cos(x-\pi)}=\frac{-\sin x}{-\cos x}=\tan x$.
Doing this $9$ times keeps the value as $\tan x$. Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C)}} \]