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

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

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

Eliminate theta , if tantheta+sintheta=x , tantheta-sintheta=y

If tantheta=b/a ,show that acos2theta+bsin2theta=a

Solve : sintheta=-1/2 , tantheta=1/sqrt3

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

Show that sectheta+tantheta=tan(pi/4+theta/2)

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)