Question

Assuming A≠0, evaluate the limit
lim 3sin^2(At) / cos(At) - 1
t-->0

Answer 1

Ok, we'll need to use a few identities.

First, apply:
\[Sin^2(\theta) = \frac{1-Cos(2 \theta)}{2}\]

Answer 2

You know what, a bit shorter way:
\[Sin^2(\theta) + Cos^2(\theta) = 1\]
\[Sin^2(\theta) = 1-Cos^2(\theta)\]

Substitute that in for your sin^2