Solve `abs[[1,costheta],[-costheta,-1]]`

Solve: tantheta+sectheta=2costheta

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

costheta[[costheta, sintheta], [-sintheta, costheta]]+sintheta[[sintheta, -costheta], [costheta, sintheta]]=

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

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

If Delta = |[1, 3costheta, 1], [sintheta, 1, 3costheta], [1, sintheta, 1]|, the maximum value of Delta is

(1+costheta)/(sintheta)=?

Prove that, 1/(costheta-cos3theta)+1/(costheta-cos5theta)+1/(costheta-cos7theta)+…+to n terms = 1/(2sintheta) [cottheta-cot(n+1)theta]

sqrt((1+costheta)/(1-costheta))=