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\begin{center}
{\Large TEST 2

Math 142}
\end{center}

\begin{itemize}
\item  Do your work on separate paper.  Show all your work and make your work neat.  
	You will be graded on both your answer and (most importantly) your work.
\item  You can use a calculator and one page of notes.
\end{itemize}



\begin{enumerate}


\item  (10 points) The double angle formulas are
\[
\sin(2t) = 2\sin t \cos t \qquad \cos(2t) = \cos^2t - \sin^2t
\]
Find formulas for $\sin(3t)$ and $\cos(3t)$.

\item (20 points) Prove or disprove the identities:
\begin{enumerate}
\item  \[ \frac{2\tan \theta}{1+\tan^2 \theta} = \sin 2\theta \]
\item  $\cos^2x - \sin^2 x = \sin x \cos x$
\end{enumerate}

\item (10 points) Simplify: \[ \sin\left( \tan^{-1}(3/x) \right) \]

\item (20 points) Solve the equations algebraically
\begin{enumerate}
\item  $2\cos(5x)\sin(5x) = -\sin(5x)$
\item  $2\sin^3x + \sin^2x = \sin x$
\end{enumerate}

\end{enumerate}

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