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am i allowed to make the top = to cos7x???

2006-10-17 12:17:27 · 3 answers · asked by rachel123go 3 in Science & Mathematics Mathematics

Please explain HOW you get to each step...!!

2006-10-17 12:34:04 · update #1

3 answers

Noting

Cos(a+b) = Cos a Cos b - Sin a Sin b
Cos(a- b) = Cos a Cos b + Sin a Sin b

Therefore, by summing the above

2 Cos a Cos b= Cos(a + b) + Cos (a -b)

Cos 4x + Cos 3x = 2 Cos7x/2 Cos x/2

Similar treatment using Sin(a -b) and Sin(a + b) and taking the difference yields

2Cos a Sin b = Sin (a+b) - Sin(a - b)

Sin 4x - Sin 3x =2 Cos7x/2Sinx/2

(cos4x + cos3x)/(sin4x - sin3x) = 2 Cos7x/2 Cos x/2/2 Cos7x/2Sinx/2

= Cot(x/2)

By the way Cos 4x + Cos 3x will generally not equal Cos 7x

2006-10-17 21:13:09 · answer #1 · answered by Anonymous · 0 0

To solve this problem, you need to know the following two equations:

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

If you set a = b = x, you can use the above equations to find a formula for sin 2x or cos 2x.

Then, if you set a = b = 2x, you can find sin 4x and cos 4x (since you already know what sin and cos of 2x are).

Finally, if you set a = 2x and b = x, you can find sin 4x and cos 4x (since you already know what sin and cos of x and 2x are).

You then have all the components of the formula you need to simplify. Presumably, this is what 'calculus' did to develop his solution (above).

2006-10-17 12:48:25 · answer #2 · answered by actuator 5 · 0 0

Cos4x + Cos 3x = 2.Cos(7x/2).Cos(x/2)--------A
.
sin4x - sin3x = 2.Cos(7x/2).Sin(x/2)-------B
.
Hence:
A/B = Cos(x/2) / Sin (x/2) = Cot(x/2)

.
Your second question: No.
Cos A + Cos B is not Cos (A+B)

2006-10-17 12:24:48 · answer #3 · answered by Calculus 5 · 0 0

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