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#