Question

What basic trigonometric identity would you use to verify that tan x cos x = sin x

Answer 1

The basic trigonometric identity you would use is
`\tan \left(x\right)=(\sin \left(x\right))/(\cos \left(x\right))`

Explanation:

To show that this identity is true you must:

• Manipulate left side
  `\tan \left(x\right)\cos \left(x\right)`

Use this basic trigonometric identity
`\tan \left(x\right)=(\sin \left(x\right))/(\cos \left(x\right))`

`\cos \left(x\right)\tan \left(x\right)=\cos \left(x\right)(\sin \left(x\right))/(\cos \left(x\right))`

• Simplify

`\cos \left(x\right)(\sin \left(x\right))/(\cos \left(x\right))=\sin \left(x\right)`

We showed that the two sides could take the same form.

Answer 2

`\bf tan(x) cos(x)=sin(x) \\\\\\ \cfrac{sin(x)}{{cos(x)}}\cdot {cos(x)}\implies sin(x)`