IIT JEE , AIEEE Forum - Mathematics , Trignometry

sachin_gupta1991

Find the value of

cos 6 X cos42 X cos66 X cos78

Angles are in degrees, X stands for multiplication.

rohitkuruvila

it is 1/16.if it is right ,i'll post the solution.

sachin_gupta1991

yes, it is 1/16. Plzz give me the solution.

rohitkuruvila

just re-arrange the elements

cos 6.cos 66.cos 42.cos 78

[(2cos 6.cos 66)(2cos 42.cos 78)]/4

[(cos 72+cos 60)(cos 120+cos 36)]/4

[{(

5 -1)/4}+{1/2}] [{-1/2}+{(

5 +1)/4}]/4

[(

5 -1+2)/4] [

5 +1-2)/4]/4

[(

5 +1)/4] [(

5 -1)/4]/4

[(

5 +1)(

5 -1)]/64

(5-1)/64

4/64

1/16

iitkgp_bipin

Good work Rohit.

Multiply cosines of 6 and 66 since their difference is 60 and cosines of 78 and 42 since their sum is 120 and then rearrange to get the result.

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