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Find the value of (cos 25^(@)+cot55^(@)...

Find the value of `(cos 25^(@)+cot55^(@))/(tan 25^(@)+tan55^(@))+(cot55^(@)+cot100^(@))/(tan55^(@)+tan100^(@))+(cot 100^(@)+cot25^(@))/(tan 100^(@)+tan 25^(@))`.

Text Solution

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`E=(cot 25^(@)+cot55^(@))/(tan 25^(@)+tan55^(@))+(cot 55^(@)+cot100^(@))/(tan55^(@)+tan 100^(@))+(cot100^(@)+cot25^(@))/(tan 100^(@)+tan25^(@))`
`=(1)/(tan 55^(@)tan 100^(@))+(1)/(tan 55^(@)tan 100^(@))+(cot 100^(@)+cot 25^(@))/(tan 100^(@)+tan 25^(@))`
`=(tan 25^(@)+tan55^(@)+tan 100^(@))/(tan 25^(@)+tan55^(@)Tan 100^(@))`
Since `25^(@)+55^(@)+100^(@)=180`
`tan 25^(@)+tan 55^(@)+tan 100^(@)=tan 25^(@)tan 55^(@)tan 100^(@)`
`rArr E=1`
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