Find the value of

Posted July 8th, 2009 by alpha

If $cos25^0+sin25^0=p$ , then find the value of $cos50^0$

Comments

On July 9th, 2009 Structure says:

$\sin a+\cos a=p$

$(\sin a+\cos a)^2=1+2\sin a\cos a=p^2$

$1-2\sin a\cos a=(\cos a-\sin a)^2=2-p^2$

$\cos 2a=(\cos a-\sin a)(\cos a+\sin a)=\pm p\sqrt{2-p^2}$

for $a=25^o$

$\cos 50^o=p\sqrt{2-p^2}$

On July 9th, 2009 alpha says:

-------------------x----------------------------
``Old theorems never die; they turn into definitions.''
----E. Hewitt

''ALPHA" =)