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cot^(2)pi/6+"cosec"(5pi)/(6) + 3tan^(2)p...

`cot^(2)pi/6+"cosec"(5pi)/(6) + 3tan^(2)pi/6=6`

Text Solution

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LHS `=cot^(2)pi/6 + "cosec"(5pi)/(6)+3tan^(2)pi/6`
`=cot^(2)pi/6+"cosec"(pi/6)+3(tanpi/6)^(2)`
`=(cot30^(@))^(2) + ("cosec"30^(@))+3(tan 30^(@))^(2)`
`=(sqrt(3))^(2)+2+3(1/sqrt(3))^(2)=3+2+1=6`
RHS Hence Proved.
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