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

If a cos theta +bsin theta=x and a sin theta-b cos theta = y then prove that a^2+b^2=x^2+y^2

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 .

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

If x=a sectheta *cosphi y=b sectheta *sinphi , z=c tantheta then prove that x^2/a^2 +y^2/b^2 -z^2/c^2 =1

If cosectheta + cottheta= k , then prove that costheta=(k^2-1) /(k^2+1)

If a costheta -b sin theta = c ,then prove that a sintheta + b costheta=+-sqrt(a^2+b^2-c^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)

If x=acostheta and y=bsintheta then the value of b^2x^2+a^2y^2 is

if costheta+sintheta=sqrt2 costheta, prove that costheta-sintheta=sqrt2sintheta