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Vsevolod [243]
2 years ago
8

Simplify the following expression to its simplest form

Mathematics
1 answer:
SashulF [63]2 years ago
5 0

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) )

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