Law of cosine

[Aladdin]

By using the law of cosine : Prove that \(\displaystyle 2a^2 = b^2 + c^2\)

If and only if : \(\displaystyle bc = \frac{a^2}{2cos(A)}\)

 

[galactus]

\(\displaystyle a^{2}=b^{2}+c^{2}-2bccos(A)\)

But \(\displaystyle 2bc\cdot cos(A)=a^{2}\)

\(\displaystyle 2bc\cdot cos(A)=b^{2}+c^{2}-2bc\cdot cos(A)\)

\(\displaystyle 2bc\cdot cos(A)+2bc\cdot cos(A)=b^{2}+c^{2}\)

\(\displaystyle 2a^{2}=b^{2}+c^{2}\)

 

[Aladdin]

Thank you Cody , you really gave me a big push on how to solve the next problems . I really thought of this idea but when I reached the 3rd step I stop , Maybe I was doing something wrong ( I don't know ) .

Thanks Again

 

[Deleted member 4993]

Remember - for if and only if - it needs to be proven both ways.

 

[Aladdin]

Remember - for if and only if - it needs to be proven both ways.

Mr Khan , I'm not done yet ?! - We used the second relation to prove the first relation , does this means that we have to use the first relation and then prove the second :?:

 

[Deleted member 4993]

Remember - for if and only if - it needs to be proven both ways.

Mr Khan , I'm not done yet ?! - We used the second relation to prove the first relation , does this means that we have to use the first relation and then prove the second :?:

Yes -

"if and only if" implies that you will have to prove both way.