Question

Evaluate . Sin ( Tan^-1 (0))

Answer 1

tan is zero when sin is zero. So, inverse tan of zero will be zero (or 180 degrees or 360 degrees or multiples of such). And, sin of any of those will be zero. So, the answer must be zero.

Answer 2

Let \[\theta=\tan^{-1} 0\]
Then \[\tan \theta=0\]So\[\theta=2pi\]So
\[\tan^{-1} 0=2pi\]\[\sin 2pi=0\]