How do you evaluate this problem?

Question

Lim ........ ____sin (x - 2)____
x=>2- ................ (x - 2)

Answer 1

put x-2=t then as x>2 the x-2 will tend to 0 or t>0
lt t>0sint/t=1 (standard limit)

Answer 2

say h = x-2
lim(x=>2) is also lim (h=>0) [ sin(h)/h ]
also
lim(h=>0) [ ( sin(h) - sin(0) )/h ]
which is also the definition of the derivative of sin(h) in 0
(sinh)' = cosh
so your answer is cos(0) = 1