Question #835cb

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Answer 1 · 2017-02-12T03:05:14

Given

#tana/tanb=sqrt3#

#=>cotb/cota=sqrt3#

#=>cotb=sqrt3cota......[1]#

Again

#sina/sinb=sqrt2#

#=>cscb/csca=sqrt2#

#=>csc^2b/csc^2a=2#

#=>(1+cot^2b)/(1+cot^2a)=2#

Putting #cotb=sqrt3cota#

#=>(1+3cot^2a)/(1+cot^2a)=2#

#=>1+3cot^2a=2+2cot^2a#

#=>3cot^2a-2cot^2a=2-1=1#

#=>cota=1=cot(pi/4)=cot(pi+pi/4)#

#=>a=pi/4 and (5pi)/4#

Inserting #a =pi/4 or (5pi)/4# in [1]

#=>cotb=sqrt3cota#

#=>cotb=sqrt3xx1=cot(pi/6)=cot(pi+pi/6)#

#=>b=pi/6 and (7pi)/6#