Distributing Cos45 in an Expression: Numerator and Denominator

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In the expression cos45[(601-148)/sin21.8], cos45 is only multiplied into the numerator, not the denominator. This is clarified by considering cos(45) as cos(45)/1, which means it affects only the numerator while the denominator remains unchanged. Distributing cos(45) to both parts would lead to cancellation, which is not the desired outcome. The discussion emphasizes the importance of correctly applying trigonometric functions in expressions. Understanding this distribution is crucial for accurate calculations in trigonometry.
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Let's say I have an expression like this.

cos45[(601-148)/sin21.8]

Does cos45 get multiplied into just the numerator terms or do I also distribute it to the denominator as well?
 
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Only the numerator. Think of it as cos(45)/1 so that cos(45) multiplies the numerator and 1 multiples the denominator.

Also, notice that cos(45) equals something simple.
 
Multiplying into the numerator and the denominator would give you \frac{cos(45)(601-148)}{cos(45)sin(21.8)} and the cosines would cancel which is not what you want.
 
Ok, thanks guys.
 
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