Hardest Identity Evar involving sum and differences

In summary, the equation sin (x) + sin (3x) + sin (5x) + sin (7x) = 4cos(x)cos(2x)sin(4x) involves using the sum and difference identities for sine to simplify the left side of the equation. By grouping terms and repeatedly applying the identities, the equation can be transformed into a simpler form.
  • #1
amd123
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Homework Statement


sin (x) + sin (3x) + sin (5x) + sin (7x) = 4cos(x)cos(2x)sin(4x)

Homework Equations


sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
sin(a-b)=sin(a)cos(b)-sin(b)cos(a)

The Attempt at a Solution


Me and four of my classmates have tried to do this proof and it kicked our ***.
Please help.
 
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  • #2
amd123 said:

Homework Statement


sin (x) + sin (3x) + sin (5x) + sin (7x) = 4cos(x)cos(2x)sin(4x)

Homework Equations


sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
sin(a-b)=sin(a)cos(b)-sin(b)cos(a)

The Attempt at a Solution


Me and four of my classmates have tried to do this proof and it kicked our ***.
Please help.

Here's what worked for me.
sin(x) + sin(3x) + sin(5x) + sin(7x) = sin(2x - x) + sin(2x + x) + sin(6x -x) + sin(6x + x)

Expand the terms on the right side, and several terms will drop out. You will need to apply the same trick again.
 

1. What is the "Hardest Identity Evar involving sum and differences"?

The "Hardest Identity Evar involving sum and differences" is a mathematical equation that challenges people to find the value of a given expression by using only addition and subtraction.

2. What makes this identity so difficult?

This identity is considered difficult because it requires a deep understanding of mathematical principles and the ability to manipulate numbers in creative ways. It also involves multiple steps and can be very time-consuming to solve.

3. Can you give an example of this identity?

Sure, an example of the "Hardest Identity Evar involving sum and differences" is: 7 + 7 - 7 + 7 - 7 + 7 = ?

4. Is there a specific strategy or approach to solving this identity?

There are many different strategies that can be used to solve this identity, but one common approach is to group the numbers into pairs and then use the property of additive inverses to simplify the expression.

5. Why is this identity important in the field of mathematics?

This identity challenges individuals to think critically and creatively, which are important skills in the study of mathematics. It also helps to strengthen problem-solving abilities and builds a strong foundation for more complex mathematical concepts.

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