Explanation:Trigonometry: Simplifying (cos A + 1) / cos A Step by Step

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The problem involves simplifying the expression (cos A + 1) / cos A. The solution shows that this can be rewritten as 1 + (1/cos A), which simplifies further to 1 + sec A. This step-by-step breakdown helps in understanding the process of reducing trigonometric expressions. The explanation emphasizes the importance of recognizing the relationship between cosine and secant in trigonometry. Overall, the simplification provides clarity for solving similar problems in the future.
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[SOLVED] Trigonometry cos A + 1

My little sis needs help w/ the following problem for her homework and to tell you the truth, aside from the fact that I'm too busy I have no idea how to explain this to her step by step. I would appreciate an explanation on how to solve it -- a solution would be fine but even just the steps for solving it would be appreciated. thanks.


Homework Statement



Reduce
(cos A + 1) / cos A
 
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The only thing I can see is the obvious:
\frac{cos A+ 1}{cos A}= 1+ \frac{1}{cos A}= 1+ sec A[/itex]
 
HallsofIvy said:
The only thing I can see is the obvious:
\frac{cos A+ 1}{cos A}= 1+ \frac{1}{cos A}= 1+ sec A[/itex]
<br /> <br /> <br /> Thank you very much. I appreciate the help.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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