I just read somwhere thatif cos a = cos dthen a=2n(pi)±d where

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In summary, the conversation discusses the relationship between cosine values and how they can be written in terms of 2n(pi)±d, where n is an integer. However, this statement is not entirely accurate, as there are exceptions such as cos(pi/2) and cos(3pi/2) being equal. The statement b*ln i/j = 2n(pi)±b*ln(j/i) is true, but not particularly informative. The last statement, b=n(pi)/(ln(i/j)+ln(j/i)), is incorrect as it involves division by zero.
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sparsh12
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i just read somwhere that

if cos a = cos d

then a=2n(pi)±d where n is integer

So, if cos (b*ln (i/j))= cos (-b (lni/j))=cos(b*ln(j/i))

can i write
b*ln i/j = 2n(pi)±b*ln(j/i)
or
bln(j/i)+bln(i/j)=2n(pi) or 2n(pi)=0
b=n(pi)/(ln(i/j)-ln(j/i))=n(pi)/(b*ln(i/j))

then replace b in
cos(b*lni/j)=cos(n(pi))= ±1

I feel that something is wrong. But what?
 
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sparsh12 said:
i just read somwhere that

if cos a = cos d

then a=2n(pi)±d where n is integer

This isn't entirely true... for example, cos(pi/2) and cos(3pi/2) are equal.

b*ln i/j = 2n(pi)±b*ln(j/i)

This is definitely true, but not as interesting as it might look at first sight. Just take n=0 and b*ln(i/j)=-b*ln(j/i) (note that the statement is a=2n(pi)+d for SOME integer n, not every integer)

b=n(pi)/(ln(i/j)+ln(j/i))=n(pi)/(b*ln(i/j))

When you divide by ln(i/j)+ln(j/i) you divided by zero. I'm unsure where your last equality comes from
 

1. What is the significance of the equation "cos a = cos d"?

This equation shows that the cosine function is an even function, meaning that it is symmetrical about the y-axis. This means that if we plug in an angle a, we will get the same output as if we plugged in -a. Similarly, if we plug in an angle d, we will get the same output as if we plugged in -d.

2. How does the equation "a = 2n(pi)±d" relate to the original equation "cos a = cos d"?

This equation is known as the periodicity formula for cosine. It shows that if we add or subtract a multiple of 2π to the angle a, we will get the same output as the angle d. This is because cosine has a period of 2π, meaning that it repeats itself every 2π units.

3. Can you provide an example of how to use the equation "a = 2n(pi)±d" to solve for a value of a given cos d?

Sure, let's say we have the equation cos a = cos (3π/4). To solve for a, we can use the periodicity formula and set n=0, since we are looking for the first possible value of a. This gives us a = 2(0)(π) ± (3π/4) = ±(3π/4). So, a can be either 3π/4 or -3π/4.

4. What does the "±" symbol mean in the equation "a = 2n(pi)±d"?

The "±" symbol means that we can use either a plus or minus sign in the equation, depending on the specific situation. In some cases, the plus sign may give us a valid solution, while in others, the minus sign may be the correct choice.

5. Can the equation "cos a = cos d" be used to solve for values of a and d other than angles?

No, this equation can only be used to solve for angles. The cosine function is only defined for angles, so any other values plugged in for a or d would not make sense in this context.

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