Substituting terms in an equation?

Questions
1

Hi,
I have this equation:

Sin[Theta]== ( c2 o1y - c1 c3 o1y + c2 o1z + c1 c2 o1z)/((c2 - c1 c3) l1);
Cos[Theta] == ( 2 c2 o1x - 2 c1 c3 o1x + o1z + c1^2 o1z - c2^2 o1z - c3^2 o1z)/(2 (c2 - c1 c3) l1);

Now i have to found this equation:

F1= Sin[Theta]^2+Cos[Theta]^2-1

but when I write it gives me back the same writing instead I want to develop all the elements, how do I do?

2

Hi Seb

Better call ist substitute terms in an expression.

ST = (c2 o1y - c1 c3 o1y + c2 o1z + c1 c2 o1z)/((c2 - c1 c3) l1);
CT = (2 c2 o1x - 2 c1 c3 o1x + o1z + c1^2 o1z - c2^2 o1z - 
     c3^2 o1z)/(2 (c2 - c1 c3) l1);

Sin[Theta]^2 + Cos[Theta]^2 - 1 /. {Sin[Theta] -> ST, Cos[Theta] -> CT}

Robert

3

Consider:

Sin[whatever]^2 + Cos[whatever]^2 - 1 // Simplify
(*   Out:  0   *)
4

Crossposted here.