Question

Let \(f : [-\frac{\pi}{2}, \frac{\pi}{2}] \rightarrow (-\infty, \infty)\) be given by \(f(x) = \tan(x)\sin(x)\). Then \(f(x)\) is

• A. an even function but not 1-1 function
• B. an odd function
• C. an even function
• D. an odd function but not an onto function
• E. 1-1 and an odd function

Hint:

The product of two odd functions is always an even function. (Odd \(\times\) Odd = Even). Since both \(\tan(x)\) and \(\sin(x)\) are odd, their product is guaranteed to be even without further calculation.

Answer 1

The Correct Option is C