If , prove that a, b, c, and d are proportionals.
We also know that if , then the property of componendo and dividendo says: . Applying this property to the above “huge” fraction, we get:
We know that if , then , which is the property called alternendo. Applying this property to the above fraction, we get
again, applying componendo and dividendo to the above, we get
hence, , that is, a, b, c and d are proportionals. Hence, the proof.
Solve the equation:
By componendo and dividendo, we get
Now, squaring both sides of the above equation, we get .
Again, applying componendo and dividendo,
so, we get
so, we get finally