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Simplify the following expression to its simplest form

Simplify the following expression to its simplest form-example-1
User Esynce
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1 Answer

11 votes

Explanation:


\sin(\pi - x) + \tan(x) \cos(x) (x - (\pi)/(2)


\sin( - x + \pi ) + \tan(x) ( \cos(x - (\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 - (\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 - (\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) )

User Volodymyr Sorokin
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