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Find the value of (tan 9^(@)+cot9^(@))/(...

Find the value of `(tan 9^(@)+cot9^(@))/(tan27^(@)+cot27^(@))`.

Text Solution

Verified by Experts

The correct Answer is:
`(3+sqrt(5))/(2)`
`(tan9^(@)+cot9^(@))/(tan27^(@)+cot27^(@))=(tan9^(@)+(1)/(tan9^(@)))/(tan27^(@)+(1)/(tan27^(@)))`
`=(Tan^(2)9^(@)+1)/(2 tan 9^(@))(2tan 27^(@))/((tan^(2)27^(@)+1)`
`=(sin 54^(@))/(sin18^(@))=(cos 36^(@))/(sin18^(@))`
`=(sqrt(5)+1)/(4).(4)/(sqrt(5)-1)`
`=(sqrt(5)+1)/(sqrt(5)-1)xx(sqrt(5)+1)/(sqrt(5)+1)=(3+sqrt(5))/(2)`.
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