# Addition/subtraction formulas for sine or cosine to simplify the following

#### math951

cos(3pi/10)cos(pi/5)-sin(3pi/10)sin(pi/5)

factor cos and sin and get common denominators and combine:

cos(5pi/10)-sin(5pi/10)

cosine(90 degrees)-sin(90 degrees)

0-1

answer is -1? Am I correct?

Wait I see the formula for this is : cos(a+b)

so then I do cos(3pi/10+pi/5)

cos(5pi/10)

and that =0? Is that how I do it?

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#### topsquark

Forum Staff
cos(3pi/10)cos(pi/5)-sin(3pi/10)sin(pi/5)

factor cos and sin and get common denominators and combine:

cos(5pi/10)-sin(5pi/10)

cosine(90 degrees)-sin(90 degrees)

0-1

answer is -1? Am I correct?

Wait I see the formula for this is : cos(a+b)

so then I do cos(3pi/10+pi/5)

cos(5pi/10)

and that =0? Is that how I do it?

-Dan

1 person

#### Debsta

MHF Helper
cos(3pi/10)cos(pi/5)-sin(3pi/10)sin(pi/5)

factor cos and sin and get common denominators and combine:

cos(5pi/10)-sin(5pi/10) No No No

cosine(90 degrees)-sin(90 degrees)

0-1

answer is -1? Am I correct? No

Wait I see the formula for this is : cos(a+b) Yes Yes Yes Stick to the rules!

so then I do cos(3pi/10+pi/5)

cos(5pi/10)

and that =0? Is that how I do it? Yes
Stick to the rules.

Last edited:
1 person

#### skeeter

MHF Helper
cos(3pi/10)cos(pi/5)-sin(3pi/10)sin(pi/5)
$\cos\left(\dfrac{3\pi}{10}\right)\cos\left(\dfrac{2\pi}{10}\right) - \sin\left(\dfrac{3\pi}{10}\right)\sin\left(\dfrac{2\pi}{10}\right) \ne \cos\left(\dfrac{5\pi}{10}\right) - \sin\left(\dfrac{5\pi}{10}\right)$

the identity is ...

$\cos{a}\cos{b} - \sin{a}\sin{b} = \cos(a+b)$

$\cos\left(\dfrac{3\pi}{10}\right)\cos\left(\dfrac{2\pi}{10}\right) - \sin\left(\dfrac{3\pi}{10}\right)\sin\left(\dfrac{2\pi}{10}\right) = \cos\left(\dfrac{3\pi}{10} + \dfrac{2\pi}{10}\right) = \cos\left(\dfrac{\pi}{2}\right) = 0$

1 person