Question

Question #75f9a

Answer 1

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