Question

Find the value of cos20°cos40ºcos60°cos80°

Answer 1

Heya buddy,

-----------------------

Here is your answer,

Question : cos20.cos40.cos60.cos80

Since, cos60 = 1/2
Therefore, 1/2×cos20×cos40×cos80
Now,
Multiply and divide by 2,

=> 1/4 (2 cos20×cos40×cos80)
=> 1/4 (cos(20+80)+ cos(20-80))×cos40
Since, (2cosa.cosb= cos(a+b) + cos(a-b))
Thus,
=> 1/4 (cos(-60) + cos(100))×cos40
=> 1/4(1/2 + cos100)×cos40
=> 1/8 cos40+ 1/4 (cos40×cos100)
Now again,
Multiply and divide by 2,
Therefore,
=> 2/2(1/8 cos40) + 1/8(2 cos40 cos100)
=> 1/8 cos40+ 1/8 (cos140+ cos(-60))
Since, (2cosa.cosb= cos(a+b)×cos(a-b))

=> 1/8 cos40+ 1/8 cos140 + 1/16
Since, (cos60= 1/2)
Therefore,
=> 1/8(cos40+cos140) + 1/16
=> 1/8(2 cos90 cos(-50)) + 1/16
Since, cos90= 0

Therefore,
The ans is 1/16

--------------------------

Hope it helps you.
Thank you.