Show that limit of Sin(x) as x approaches a = Sin (a). Help!

[Dhartju]

Given that limit of sin(x) as x approaches 0 = 0 and limit of cos(x) as x approaches 0 = 1, show that limit of sin(x) as x approaches a = sin(a) for any real number a (i.e. show that the sine function is continuous on R. Note you may not use continuity in your proof.)
I'm having trouble of showing proof for this statement. Thank you all in advance!

 

[stapel]

Given that limit of sin(x) as x approaches 0 = 0 and limit of cos(x) as x approaches 0 = 1, show that limit of sin(x) as x approaches a = sin(a) for any real number a (i.e. show that the sine function is continuous on R. Note you may not use continuity in your proof.)

I'm having trouble of showing proof for this statement. Thank you all in advance!

What have you tried? Where are you stuck? Does this discussion reflect the sort of reasoning that you're being expected to do?

Thank you!