Question

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

Answer 1

`\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)