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

Solve sin2theta+costheta=0

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

Prove that (1+sintheta-cos theta)/(1+sin theta+costheta)=tantheta//2

If A=[(costheta,sintheta),(-sintheta,costheta)] Find A^2

Solve costheta+cos3theta-2cos2theta=0 .

Simplify costheta[[costheta, sin theta],[-sintheta, costheta]]+sintheta[[sintheta, -costheta],[costheta, sintheta]]

Prove that abs(costheta-isintheta) = 1

Prove that sintheta+sin3theta+sin5theta+sin7theta=4costhetacos2thetasin4theta

solve sqrt3 costheta+sintheta=sqrt2