If `cosectheta-sintheta=m`and `sectheta-costheta=n`,show that `(mn)^(2//3)(m^(2//3)+n^(2//3))=1`

if tantheta+sintheta=m and tantheta-sintheta=n show that (m^2-n^2)^2=16mn

If sintheta +costheta =p and sectheta+cosectheta=q , show that q(p^2 -1)=2p .

If tantheta +sintheta=m and tantheta-sintheta=n prove that m^2-n^2=4sqrt(mn)

If tan theta+sin theta =m and tan theta-sin theta=n ,then show that m^2-n^2=4sqrt(mn) .

If ay costheta=bxsintheta and axsectheta-by cosectheta=a^2-b^2 ,prove that x^2/a^2+y^2/b^2=1

If (ax)/costheta+(by)/(sintheta)=a^2-b^2 and (axsintheta)/cos^2theta-(bycostheta)/sin^2theta=0 ,show that (ax)^(2//3)+(by)^(2//3)=(a^2-b^2)^(2//3)

Evaluate : |(2costheta, -2sintheta),(sintheta, costheta)| .

If a costheta-b sintheta=c ,show that a sintheta+bcostheta=+-sqrt(a^2+b^2-c^2)

Solve: 2cos^2theta-3costheta+1=0

Prove the following (cosectheta-sintheta)(sectheta-costheta)=1//(tantheta+cottheta)