Prove that the determinant `[xsinthetacostheta-sintheta-x1costheta1x]`is independent of 0.

Prove that the determinant [(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x)] is independent of theta .

Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]| is independent of theta

Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),(cos theta,1,x)| is independent of theta

Prove that the determinant Delta =|{:(x,,sintheta,,cos theta),(-sin theta,,-x,,1),(cos theta,,1,,x):}| is independent of theta .

If |[x,sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]|=8 , write the value of xdot

Prove that (1-sintheta+costheta)^2=2(1+costheta)(1-sintheta)

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tantheta/2

Prove that (costheta-sintheta+1)/(costheta+sintheta-1)=c o s e ctheta+cottheta

Prove that : (1+sintheta)/(costheta)+(costheta)/(1+sintheta)=2sectheta

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)