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If X is A.M. of tan(pi/9) and tan ((5pi...

If X is `A.M.` of `tan(pi/9)` and `tan ((5pi)/18)` and `y` is `A.M.` of `tan(pi/9)` and `tan((7pi)/18)`, then

Text Solution

Verified by Experts

The correct Answer is:
y=2x
`2x=tan20^(@)+tan50^(@)`
`=(sin(20^(@)+50^(@)))/(cos20^(@)cos50^(@))`
`=(sin70^(@))/(sin70^(@)tan40^(@))=(1)/(sin40^(@))`
`2y=tan20^(@)=tan70^(@)`
`=(sin(20^(@)+70^(@)))/(cos20^(@)cos70^(@))`
`=(2)/(2cos 20^(@)sin20^(@))=(2)/(sin40^(@))`
`therefore y=(1)/(sin40^(@))=2x`
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