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:

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

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)