SOLUTION: if 3 sin theta-4 cos theta=5 find the value of (3 sin theta + 4 cos theta)

Divide through by 5

 

Let  and  using this right triangle:



 

Multiply through by -1 and reverse terms on the left:

 

Now we recognize the left side as the identity for .

 

So 

   , k an odd number

   

We want to find the value of  , so

 



            and  since k is odd.  So the above becomes:





And by the right triangle above that equals



Edwin