In any triangle ABC, prove the following:
Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get
⇒ a = k sin A, b = k sin B, c = k sin C
Now,
Substituting the values from sine rule into the above equation, we get
But
And
And
Substituting these we get
By canceling the like terms, we get
Similarly,
Substituting the values from sine rule into the above equation, we get
But
And
And
Substituting these we get
By canceling the like terms, we get
Similarly,
Substituting the values from sine rule into the above equation, we get
But
And
And
Substituting these we get
By canceling the like terms, we get
So the LHS of the given equation, we get
From equation (i), (ii) and (iii), we get
Hence proved