# COS10*COS30*COS60*COS70=(3/16) SOLVE IT HOW TO SOLVETHIS QUESTION

Himanshu
103 Points
7 years ago
Your question is definitely wrong. It must be as follows:-
cos10.cos30.cos50.cos70 = 3/16
L.H.S. = cos30.cos10.cos50.cos70
= root(3)/2 × cos10.cos50.cos70
= root(3)/4 × (cos60 + cos40)cos70
= root(3)/8 × 2cos60.cos70 + 2cos40.cos70
= root(3)/8 × (cos70 + cos110 + cos30)
= root(3)/8 × (cos70 - cos70 + root(3)/2)
= [root(3) × root(3)] / (8×2)
= 3/16 = R.H.S.
Hence, proved.
3 years ago
Dear student,

The question seems wrong as the answer for the said question would be different around 2.33/16, you can check it by calculator.
Coming back to the the question it might actually be

cos10.cos30.cos50.cos70 = 3/16
L.H.S. = cos30.cos10.cos50.cos70
= root(3)/2 × cos10.cos50.cos70
= root(3)/4 × (cos60 + cos40)cos70
= root(3)/8 × 2cos60.cos70 + 2cos40.cos70
= root(3)/8 × (cos70 + cos110 + cos30)
= root(3)/8 × (cos70 - cos70 + root(3)/2)
= [root(3) × root(3)] / (8×2)
= 3/16 = R.H.S.
Hence, proved.

Hope it helps.
Thanks and regards,
Kushagra