Question

Simplify the following expression to its simplest form

Answer 1

Step-by-step explanation:

$\sin(\pi - x) + \tan(x) \cos(x) (x - \frac{\pi}{2}$

$\sin( - x + \pi ) + \tan(x) ( \cos(x - \frac{\pi}{2} ) )$

Sin is odd function, so if you add pi to it, it would become switch it sign.

$- \sin( - x) + \tan(x) \cos(x - \frac{\pi}{2} )$

Also since sin is again, a odd function, we can just multiply the inside and outside by -1, and it would stay the same.

$\sin(x) + \tan(x) \cos(x - \frac{\pi}{2} )$

Cosine is basically a sine function translated pi/2 units to the right or left so

$\sin(x) + \tan(x) \sin(x)$

$\sin(x) ( 1 + \tan(x) )$