Question

Cos6 . Cos42 . Cos66 . Cos78=?

Answer 1

just trying..
cos 6 = sin 84 = 2sin 42 cos 42....

Answer 2

(78-66) /2 =6
so maybe 2 cos C cos D formula...

Answer 3

(cos 6) (cos 42)(cos 66) (cos 78) = (1/4) * (cos72 + cos60) * (cos120 + cos36)
= (1/4) (cos72 + 1/2) * (- 1/2 + cos36)
=(1/4)( cos 72 cos36 + 1/2( cos 36- cos72) -1/4 )
use formula for cos a- cos b ,
= 1/4 ( 2 sin54 sin18 -1/4)
=1/4 ( sin36 sin54/ cos 18 -1/4)
= 1/4( cos 18 - cos 90) / 2cos18 -1/4)

= ans

this might seem tedious to read at first, but i believe 've done it correctly.. please reply..

Answer 4

are u sure u typed the qustion properly? isn't there any + or _ sign

Answer 5

Nah..! Question is Correct

Answer 6

i think i got it :)
use the formula this :
--------------------------------------------
cos(a) . cos(60-a) . cos(60+a) = [cos(3a)]/4
-------------------------------------------
set a = 6
cos(6) . cos(54) . cos(66) = cos(18)/4
so, cos(6) . cos(66) = cos(18)/(4 * cos(54)) .... (1)
set a = 18
cos(18) . cos(42) . cos(78) = cos(54)/4
so, cos(42) . cos(78) = cos(54)/(4 . cos(18)) .... (2)

multiply both, giving us :
cos(6) cos(42) cos(66) cos(78) = 1/16 * cos(18)cos54/(cos(18)*cos(54)
= 1/16 * 1
= 1/16

Answer 7

Yup...Thats Correct...thxx.)

Answer 8

welcome, :)

Answer 9

even my ans yielded 1/16 ! voila!
seems i complicated it too much! :P