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.

SALUTES ASSURED TO ALL CORRECT ANSWERS.

srujana

cos 6 . cos42. cos66 . cos78

rearranging

cos 6 . cos66. cos42 . cos78

= (cos 120 + cos 36)(cos 72+cos 60) /4

=(-1-

5)/4 (

5+1)/4 .1/4

= (-3-

3)/32

rtiit

is it 1/16??????//

nadeemoidu

Use the formula cos A cos( 60 + A ) cos ( 60 - A ) =(1/4) cos 3A

manoj_babu

we know that cx.c60+x.c60-x=1/4c3x

c6.c66.c78.c42

=>sec54.1/4c18.c78.c42

=>sec54.1/16cos54

=>1/16

pramit

it is 0.0625

nivedh_89

cos 6 . cos42. cos66 . cos78 = cos 6 . cos66. cos42 . cos78

= (cos 120 + cos 36)(cos 72+cos 60) /4

now we know that,
cos120 = -0.5
cos36 = (

5 + 1)/4
cos72 = (

5 - 1)/4
cos60 = 0.5..........!!!!!!!!!!
substituting these values,

(cos 120 + cos 36)(cos 72+cos 60) /4 =
((

5 + 1)/4 - 1/2)*((

5 - 1)/4 + 1/2)*1/4 = 1/16.........!!!!

rsharma.ranchi_000

HI.......

DEAR,

cos 6 . cos42. cos66 . cos78

=[1/2]x[2.(cos6).cos(66)]x[1/2]x[2.(cos42).cos(78)]

= (cos 120 + cos 36)(cos 72+cos 60) /4

[since 2.cosA.cosB = { cos(A-B)+cos(A+B) }]

=(-1-5)/4 (5+1)/4 .1/4

= (-3- 3)/32

deedee

hi

change d angles into radians

if the denominator is odd

then d formula is 1/2^n......(see d article posted by himanshu on shortcuts)

where n is d no. of terms

here there r 4 terms

thus 1/2^4

=1/16

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