# Cosine law

• Sep 6th 2011, 12:19 PM
mido22
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\$
• Sep 6th 2011, 11:27 PM
Opalg
Re: want help in cosine law
Quote:

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\$.
• Sep 7th 2011, 03:08 PM
mido22
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 )\$
• Sep 7th 2011, 03:25 PM
pickslides
Re: want help in cosine law
Quote:

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?
• Sep 7th 2011, 03:35 PM
mido22
Re: want help in cosine law
no i can't say so becz a!=b
• Sep 7th 2011, 04:22 PM
skeeter
Re: want help in cosine law
Quote:

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\$
• Sep 7th 2011, 04:25 PM
mido22
Re: want help in cosine law
and how can i get a=b from same problem