If `P+Q=(7pi)/(6)`, then find the value of `(sqrt(3)+tanP)xx(sqrt(3)+tanQ)`.

Answer

4

Explanation

We have `P+Q=210^(@)`
` rArr ( sqrt 3 + tan P ) ( sqrt 3 + tan Q)`
`rArr(sqrt(3)+tanP)(sqrt(3)+tan(210^(@)-P))`
`=(sqrt(3)+tanP)(sqrt(3)tan(30^(@)-P))`
`=(sqrt(3)+tanP)(sqrt(3)+(((1)/sqrt(3)-tanP))/((1+(1)/sqrt(3)tanP)))`
` " " = ( sqrt 3 + tan P ) ( sqrt 3 + ( 1- sqrt3 * tan P)/( sqrt 3 + tan P ))`
`=4`