Question

Verify the identity.\\ $\sin 2x + \cos 2x \cot 2x = \csc 2x$\\ $\sin 2x + \cos 2x \cot 2x = \sin 2x + \cos 2x \cdot \frac{\cos 2x}{\sin 2x}$ \\ $= \frac{\sin^2 2x + \cos^2 2x}{\sin 2x}$ \\ $= \frac{1}{\sin 2x}$ \\ $= \csc 2x$

          Verify the identity.\\
$\sin 2x + \cos 2x \cot 2x = \csc 2x$\\
$\sin 2x + \cos 2x \cot 2x = \sin 2x + \cos 2x \cdot \frac{\cos 2x}{\sin 2x}$ \\
$= \frac{\sin^2 2x + \cos^2 2x}{\sin 2x}$ \\
$= \frac{1}{\sin 2x}$ \\
$= \csc 2x$

Verify the identity.

sin 2x + cos 2x cot 2x = csc 2x

sin 2x + cos 2x cot 2x = sin 2x + cos 2x ·(cos 2x)/(sin 2x)

= (sin^2 2x + cos^2 2x)/(sin 2x)

= (1)/(sin 2x)

= csc 2x

Added by Joseph G.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Steven Clarke

06/19/2022

Step 1

Step 1: Start with the given equation: sin^2x + cos^2x cot^2x = csc^2x Show more…

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Texts: Verify the identity. sin^2x + cos^2x cot^2x = csc^2x sin^2x + cos^2x cot^2x = sin^2x + cos^2x Verify the identity sin^2x cos^2x cot^2x = csc^2x sin^2x + cos^2x cot^2x = sin^2x + cos^2x X sin(2x) cos^2(2x) sin^2x csc^2x