another easy trig problem...

hello again!

ok, so here's a problem where it asks to change the equation so that "only one trigonometric ratio is present."

the equation is...

$\displaystyle sin\Theta=cos\Theta$

now, i'm only aware of one trig. identity that explains sin in terms of cos and it is called a half-angle identity.

and it looks like this...

$\displaystyle sin\dfrac{\Theta}{2}=\pm\sqrt\dfrac{1-cos\Theta}{2}$

Is this the identity i would use so that only one trig. ratio is present?

if so, could i just say...

$\displaystyle sin\Theta=\pm\sqrt\dfrac{1-cos2\Theta}{2}$

or maybe...

$\displaystyle sin\Theta=\pm2\sqrt\dfrac{1-cos\Theta}{2}$