Question

The expression sinx (cosx cotx- sinx) simplifies to ____?

A. cos(2x)
B. 1
C. cot2x - sin2x

Answer 1

A. cos(2x)

Explanation:

`\sin \: x( \cos \: x \: \cot \: x - \sin \: x) \\ \\ = \sin \: x \bigg( \cos \: x * \: ( \cos \: x)/(\sin \: x) - \sin \: x \bigg) \\ \\ = \cancel{ \sin \: x} \bigg(\frac{ \cos^(2) \: x - \sin^(2)x}{\cancel{\sin \: x}} \bigg) \\ \\ = \cos^(2) \: x - \sin^(2) x\\ \\ = \cos(2x)`