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The expression sinx(cosx cotx- sinx) simplifies to ___? ? O A. cos(2x) O B. cotax- sin2x Х O c. 1 SU

The expression sinx(cosx cotx- sinx) simplifies to ___? ? O A. cos(2x) O B. cotax-example-1

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\sin x(\cos (x)\cot (x)-\sin (x))

Express cot(x) as:


\begin{gathered} \cot (x)=(\cos (x))/(\sin (x)) \\ so\colon \\ \sin x(\cos (x)(\cos (x))/(\sin (x))-\sin (x)) \end{gathered}

Use distributive property:


\cos (x)^2-\sin ^2(x)

Using the double angle identity:


\cos ^2(x)-\sin ^2(x)=\cos (2x)

Answer:

cos(2x)

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