1. ## Cosine law

Q : if $\displaystyle Cos B / a = Cos A / b$
Prove that : $\displaystyle a=b$ and $\displaystyle c^2$$\displaystyle =$$\displaystyle a^2$$\displaystyle +$$\displaystyle b^2$

2. ## Re: want help in cosine law

Originally Posted by mido22
Q : if $\displaystyle Cos B / a = Cos A / b$
Prove that : $\displaystyle a=b$ and $\displaystyle c^2$$\displaystyle =$$\displaystyle a^2$$\displaystyle +$$\displaystyle b^2$
What have you tried? You could start by using the cosine rule to express cos A and cos B in terms of a, b and c. Then try to simplify the resulting equation.

Edit. After checking the question, I think that you have stated it wrongly. It should say

Prove that : $\displaystyle a=b$ or $\displaystyle c^2=a^2+b^2$.

3. ## Re: want help in cosine law

yes it is or not and i made alot of tries but all reach to same result :
$\displaystyle b^2$$\displaystyle ($$\displaystyle c^2$$\displaystyle -$$\displaystyle b^2$$\displaystyle ) =$$\displaystyle a^2$$\displaystyle ($$\displaystyle c^2$$\displaystyle -$$\displaystyle a^2$$\displaystyle ) 4. ## Re: want help in cosine law Originally Posted by mido22 yes it is or not and i made alot of tries but all reach to same result : \displaystyle b^2$$\displaystyle ($$\displaystyle c^2$$\displaystyle -$$\displaystyle b^2$$\displaystyle ) =$$\displaystyle a^2$$\displaystyle ($$\displaystyle c^2$$\displaystyle -$$\displaystyle a^2$$\displaystyle )$
Can you say a=b from this?

5. ## Re: want help in cosine law

no i can't say so becz a!=b

6. ## Re: want help in cosine law

Originally Posted by mido22
yes it is or not and i made alot of tries but all reach to same result :
$\displaystyle b^2$$\displaystyle ($$\displaystyle c^2$$\displaystyle -$$\displaystyle b^2$$\displaystyle ) =$$\displaystyle a^2$$\displaystyle ($$\displaystyle c^2$$\displaystyle -$$\displaystyle a^2$$\displaystyle )$
$\displaystyle b^2(c^2-b^2) = a^2(c^2-a^2)$

$\displaystyle b^2c^2 - b^4 = a^2c^2 - a^4$

$\displaystyle b^2c^2 - a^2c^2 = b^4 - a^4$

$\displaystyle c^2(b^2 - a^2) = (b^2 - a^2)(b^2 + a^2)$

since $\displaystyle a \ne b$ ...

$\displaystyle c^2 = b^2 + a^2$

7. ## Re: want help in cosine law

and how can i get a=b from same problem