what is cos( π/12) given that π/12 = π/3 - π/4 and that cos(a-b) = (cos a)(cos b) + (sin a)(sin b) ?

Mathematics
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what is cos( π/12) given that π/12 = π/3 - π/4 and that cos(a-b) = (cos a)(cos b) + (sin a)(sin b) ?

Apr 4th, 2015

Cos ( 360/12) = cos( 30 ) = root3/2

cos ( a - b ) = cos a . cos b + sin a . sin b

= cos pi/3. cos pi/4 + siin pi / 3 . sin pi/4

= cos 60 . cos 45 + sin 60 . sin 45

= 1/2 . 1/root2 + root 3/2 . 1/root 2

=  root3/2

Apr 4th, 2015

Cos ( 360/12) = cos( 30 ) = root3/2

...................................................................

cos ( a - b ) = cos a . cos b + sin a . sin b

= cos pi/3. cos pi/4 + siin pi / 3 . sin pi/4

= cos 60 . cos 45 + sin 60 . sin 45

= 1/2 . 1/root2 + root 3/2 . 1/root 2

= 1/root2 { 1/2 + root3 / 2 )

= 1/root 2 { (1 + root 3) / 2 }......................Answer

Apr 4th, 2015

Please consider the second solution !!!

Apr 4th, 2015

Thank you for your solution! But isn't cos( π/12) = cos(180/12) =cos(15) ? And then like what you wrote,

= 1/2 . 1/root2 + root 3/2 . 1/root 2      

then the answer should be ( root6 + root2) /4  


Apr 4th, 2015

Yes I wrote that by mistake.

Please improve it, apologies for it.

Apr 4th, 2015

Yes I wrote that by mistake.

Please improve it, apologies for it.

Apr 4th, 2015

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