Question #75f9a

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Answer 1 · 2016-11-23T16:28:31

Given $tan(alpha-beta)=7/24 and tanalpha=4/3$

So $(tanalpha-tanbeta)/(1+tanalphatanbeta)=7/24$

$=>(4/3-tanbeta)/(1+4/3tanbeta)=7/24$

$=>32-24tanbeta=7+28/3tanbeta$

$=>100/3tanbeta=25$

$=>tanbeta=3/4$

So $cotalpha =3/4 and cotbeta=4/3$

Now

$cot(alpha+beta)=(cotalphacotbeta-1)/(cotbeta+cotalpha)$

$=>cot(alpha+beta)=(3/4xx4/3-1)/(4/3+3/4)=0=cot(pi/2)$

$=>alpha+beta=pi/2$

proved