1.

If alpha and beta are roots of equation 3/4"sin"((theta)/9)=sin^(3)theta+3sin^(3)((theta)/3)+9sin^(3)((theta)/9)+1/(4sqrt(2)) for 0lt theta lt (pi)/2, then tanalpha+tanbeta is equal to

Answer»

`2+SQRT(3)`
`3+sqrt(3)`
`3-sqrt(3)`
`2-sqrt(3)`

Solution :`:.1/4 sin 3 theta=3/4sin((theta)/9)-sin^(3) theta-3"sin"^(3)(theta)/3-9sin^(3)((theta)/9)`
`IMPLIES sin 3theta=1/(sqrt(2))="sin"(pi)/4` or `"sin"(3pi)/4`
`implies theta=(pi)/12` or `(pi)/4`
`:."tan"(pi)/12=2-sqrt(3)`or `"tan"(pi)/4=1`
`:."tan"(pi)/12+"tan"(pi)/4=3-sqrt(3)`


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