` cos 20^(@) + cos 100^(@) +cos140^(@)` किसके तुल्य है ?

Options

A. 2
B. 1
C. `1//2`
D. 0

Answer

D

Explanation

` cos 2 0 ^(@) + cos 100^(@) + cos 140^(@)`
` = ( cos 140^(@) +cos 20^(@)) + cos 100^(@)`
` = 2cos . ( (140^(@)+20^(@))/2)*cos ((140^(@)-20^(@))/2)`
` + cos 100^(@)`
`= 2 cos (80^(@))* cos 60^(@) + cos 100^(@)`
` = 2 cos 80^(@) * 1/2 + cos 100^(@)`
` = cos 80^(@) +cos 100^(@)`
` = 2 cos. ((80^(@)+100^(@))/2) *cos ((100^(@) - 80^(@))/2)`
` = 2 cos 90^(@) * cos 10^(@) = 2xx0xxcos 10^(@)`
= 0