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: Use periodicity
\(\tan(\theta+n\pi)=\tan\theta\) for every integer \(n\). The period of tangent is \(\pi\).

Step 2: Apply
Here \(n=-9\), so \(\tan(x-9\pi)=\tan x\). Option (C).
Option (A) and (B) would need a sign change or a swap to cotangent, which happens for shifts by \(\frac{\pi}{2}\) not \(\pi\).

Final Answer:
\(\tan(x-9\pi)=\tan x\), option (C). \[ \boxed{\text{(C) } \tan x} \]