How do you find the value of $cos105$ without using a calculator?

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Answer 1 · 2018-03-26T06:34:27

$cos105$ = $(1-sqrt3)/(2sqrt2)$

You can write $cos(105)$ as $cos(45+60)$
Now, $cos(A+B)=cosAcosB-sinAsinB$

So, $cos(105)=cos45cos60-sin45sin60$

= $(1/sqrt2)*(1/2)-(1/sqrt2)((sqrt3)/2)$

= $(1-sqrt3)/(2sqrt2)$

How do you find the value of cos105cos105 without using a calculator?