SOLUTION: If tan 𝛼 = − 12/35 and cot 𝛽 = 3/4 for a second-quadrant angle 𝛼 and a third-quadrant angle 𝛽, find the following. (a) sin(𝛼 + 𝛽) (c) tan(𝛼 + 𝛽

Pay no attention to what that NUT is trying to "sell" you! It's nothing but sheer RUBBISH! Is she ever going to learn?

You may have noticed the following:
1) Length of the hypotenuse can NEVER be negative.
2) , which is NOT , as that person suggests. And, As a matter
of fact, this calculates to 0, although presented in a RIDICULOUS manner (), instead of , etc.
Why would someone have 0 as a denominator? Is that EVER permissible? Some of the things I see on here are as dumb as things can ever be!

If you want correct answers, then read on! 
Required: sin (𝛼 + 𝛽), and: sin (𝛼 + 𝛽) = sin 𝛼 cos 𝛽 + cos 𝛼 sin 𝛽 
. We can see that sin 𝛼, cos 𝛼, sin 𝛽 and cos 𝛽 are needed.

Given:  in the 2nd Quadrant
This is one of the Pytahorean Triples, of the form: 12-35-37. Therefore, hypotenuse = r = 37.
We therefore get: 

           Given:  in the 3rd Quadrant
This is one of the Pytahorean Triples, of the form: 3-4-5. Therefore, hypotenuse = r = 5.
We therefore get: 


So, sin (𝛼 + 𝛽) = sin 𝛼 cos 𝛽 + cos 𝛼 sin 𝛽 
 
       
                    


        

So, cos (𝛼 + 𝛽) = cos 𝛼 cos 𝛽 - sin 𝛼 sin 𝛽