Cos20cos30 + sin20sin30 ?

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Answer 1 · 2018-02-28T15:16:51

See explanation...

Alright, this is one of the 3 massive fundamental rules of trigonometry. There three rules are:

1) #sin^2x+cos^2x=1#

2) #sin(A+B)=sinAcosB+cosAsinB#

3) #cos(A+B)=cosAcosB-sinAsinB#

Rule three here is interesting because this can also be written as

#cos(A-B)=cosAcosB+sinAsinB#

This is true because #sin(-B)# can also be written as #-sinB#

Alright, now that we understand that, lets plug in you number to the formula. In this case, #A=20# and #B=30#

#cos(20-30)=cos20cos30+sin20sin30#

#=cos(-10)#

So the final answer is #cos(-10)# which approximately equals #0.98480775#

Hope this helped!
~Chandler Dowd