Cos20cos30 + sin20sin30 ?

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Answer 1 · 2018-02-28T15:16:51

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

1) ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x+cos^2x=1$

2) $sin (A + B) = sin A cos B + cos A sin B$ $sin(A+B)=sinAcosB+cosAsinB$

3) $cos (A + B) = cos A cos B - sin A sin B$ $cos(A+B)=cosAcosB-sinAsinB$

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

$cos (A - B) = cos A cos B + sin A sin B$ $cos(A-B)=cosAcosB+sinAsinB$

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

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

$cos (20 - 30) = cos 20 cos 30 + sin 20 sin 30$ $cos(20-30)=cos20cos30+sin20sin30$

$= cos (- 10)$ $=cos(-10)$

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

Hope this helped!
~Chandler Dowd