Which of the following expressions are identical
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Which of the following expressions are identical

[From: ] [author: ] [Date: 12-08-27] [Hit: ]
b) arcsin x , c) sin x^-1 ,Can you explain?-1. a) cos^2x and b) (cosx)^2 are the same, simply because that is the definition of cos^2x.......
1. a) cos²x , b) (cos x)² , c) cos x²

2. a) (sin x)^-1 , b) arcsin x , c) sin x^-1 , d) 1/sin x

Can you explain?

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1. a) cos^2x and b) (cosx)^2 are the same, simply because that is the definition of cos^2x. cos(x^2), however, is different because it is changing the argument of (what you put in to) a function, which can not be treated algebraically.
2. a) (sinx)^-1 and d) 1/sinx. Again, this simply has to do with the definition of the function. Is the entire function is raised to the power -1, it is the same as dividing it into 1. The arcsine is an inverse function, which means it undoes what the sin function calculates. c) changes the argument of the function again, so it is different from a) and d).
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