If $tan theta = 5/6$ and $tan phi= 1/11$ then find $tan (theta + phi)$ hence show that $(theta + phi) = (pie)/4$ ?

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Answer 1 · 2018-05-21T16:26:34

Proved as described below.

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$tantheta=5/6$

$tanphi=1/11$

$tan(theta+phi)=(tantheta+tanphi)/(1-tanthetatanphi)$

$=(5/6+1/11)/(1-5/6xx1/11)$

$=((5xx11+1xx6)/(6xx11))/((6xx11-5xx1)/(1xx6xx11))$

$=((55+6)/66)/((66-5)/66)$

$=61/61=1$

$tan(theta+phi)=1$

$tan(pi/4)=1$

$theta+phi=pi/4$

If tan theta = 5/6tan theta = 5/6 and tan phi= 1/11tan phi= 1/11 then find tan (theta + phi)tan (theta + phi) hence show that (theta + phi) = (pie)/4(theta + phi) = (pie)/4 ?