Question

Show that the following statement is an identity by transforming the left side into the right side.\\ $\frac{\csc \theta}{\cot \theta} = \sec \theta$\\ We begin by writing the left side in terms of $\sin \theta$ and $\cos \theta$. We can then simplify the compound fraction, and rewrite in terms of $\sec \theta$.\\ $\frac{\csc \theta}{\cot \theta} = \frac{\frac{1}{\sin \theta}}{\frac{\cos \theta}{\sin \theta}} = \frac{1}{\sin \theta \cos \theta} = \frac{1}{\cos \theta} = \sec \theta$\\ Because we have succeeded in transforming the left side into the right side, we have shown that the statement $\frac{\csc \theta}{\cot \theta} = \sec \theta$ is an identity.

          Show that the following statement is an identity by transforming the left side into the right side.\\
$\frac{\csc \theta}{\cot \theta} = \sec \theta$\\
We begin by writing the left side in terms of $\sin \theta$ and $\cos \theta$. We can then simplify the compound fraction, and rewrite in terms of $\sec \theta$.\\
$\frac{\csc \theta}{\cot \theta} = \frac{\frac{1}{\sin \theta}}{\frac{\cos \theta}{\sin \theta}} = \frac{1}{\sin \theta \cos \theta} = \frac{1}{\cos \theta} = \sec \theta$\\
Because we have succeeded in transforming the left side into the right side, we have shown that the statement $\frac{\csc \theta}{\cot \theta} = \sec \theta$ is an identity.

$Show that the following statement is an identity by transforming the left side into the right side. (cscθ)/(cotθ) = secθ We begin by writing the left side in terms of sinθ and cosθ. We can then simplify the compound fraction, and rewrite in terms of secθ. (cscθ)/(cotθ) = ((1)/(sinθ))/((cosθ)/(sinθ)) = (1)/(sinθcosθ) = (1)/(cosθ) = secθ Because we have succeeded in transforming the left side into the right side, we have shown that the statement (cscθ)/(cotθ) = secθ is an identity.$

Added by Joanne L.

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