If `cos A=-12/13` and `cotB=24/7` where `A` lies in second quadrant and `B` lies in third quadrant then find the values of `(i) sin (A+B) (ii) cos(A+B) (iii) tan(A+B)`

Explanation

Given `cos A=-12/13`,`cotB=24/7` ⟹`tanB=7/24`
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As A lies in second quadrant =`tanA<0`

So `tanA=(−sqrt(13^2−12^2))/12`

​​=`−5/12`
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As we know that

` sin (A + B) = sin A cos B + cos A sin B`

Therefore, `sin (A + B) = sin A cos B + cos A sin B `

=` 5/13 xx (-24/25) + (-12/13) xx (-7/25) `

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