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If 3tan(theta-15^0)=tan(theta+15^0), the...

If `3tan(theta-15^0)=tan(theta+15^0),` then `theta` is equal to `n in Z)` n`pi+pi/4` (b) `npi+pi/8` `npi+pi/3` (d) none of these

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`3tan(theta-15^@) = tan(theta+15^@)`
`=>(tan(theta+15^@))/(tan(theta-15^@)) = 3/1`
Using componendo and dividendo,
`=>(tan(theta+15^@)+tan(theta-15^@))/(tan(theta+15^@)-tan(theta-15^@)) = (3+1)/(3-1)`
`=>(sin(theta+15^@)/cos(theta+15^@)+sin(theta-15^@)/cos(theta-15^@))/(sin(theta+15^@)/cos(theta+15^@)-sin(theta-15^@)/cos(theta-15^@)) = 2`
`=>(sin(theta+15^@)cos(theta-15^@)+sin(theta-15^@)cos(theta+15^@))/(sin(theta+15^@)cos(theta-15^@)-sin(theta-15^@)cos(theta+15^@)) = 2`
`=>(sin(theta+15^@+theta-15^@))/(sin(theta+15^@-theta+15^@)) = 2`
`=>(sin2theta)/(sin30^@) = 2`
...
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Knowledge Check

  • If 3 tan (theta-15^(@))=tan(theta+15^(@)), 0lt thetalt pi,then theta=

    A
    `(pi)/(2)`
    B
    `(pi)/(4)`
    C
    `(3pi)/(4)`
    D
    `(pi)/(6)`

  • tan ((pi)/(4)+theta) tan ((3pi)/( 4) + theta) is equal to

    A
    `-2`
    B
    `-1`
    C
    1
    D
    0

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