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

1 Answer

Mar 26, 2018

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

Explanation:

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)#

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