Step-by-step explanation:
[tex] \sin(\pi - x) + \tan(x) \cos(x) (x - \frac{\pi}{2} [/tex]
[tex] \sin( - x + \pi ) + \tan(x) ( \cos(x - \frac{\pi}{2} ) )[/tex]
Sin is odd function, so if you add pi to it, it would become switch it sign.
[tex] - \sin( - x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]
Also since sin is again, a odd function, we can just multiply the inside and outside by -1, and it would stay the same.
[tex] \sin(x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]
Cosine is basically a sine function translated pi/2 units to the right or left so
[tex] \sin(x) + \tan(x) \sin(x) [/tex]
[tex] \sin(x) ( 1 + \tan(x) )[/tex]
