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The value of sec 20+sec 40 + sec 160 is...

The value of `sec 20+sec 40 + sec 160` is

Text Solution

Verified by Experts

`sec40+sec80=1/cos40+1/cos80`
`=(cos40+cos80)/(cos40cos80)`
`=(2cos60*cos20)/(1/2*cos120+cos40)`
`=(4*1/2*cos20)/(cos40-1/2)`
`(4cos(20))/((2cos40)-1)`
`(4cos20)/(2cos40-1)+1/cos160`
`(4cos20)/(2cos40-1)-1/cos20`
`=(4cos^2(20)-2cos(40)+1)/((2cos40-1)cos20)`
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