Question

Eliminate'theta'from the equations i) m=cosec theta-sin theta n=cosec theta+sin theta​

Answer 1

Answer:

$Given cosecθ−sinθ=m or  sinθ1−sinθ=m</p><p>or  sinθ1−sin2θ=m or sinθcos2θ=m          (i)</p><p>Again   secθ−cosθ=n or cosθ1−cosθ=n</p><p>or  cosθ1−cos2θ=n or</p><p></p><p>cosθsin2θ=n          (ii)</p><p>From Eq. (i),   sinθ=mcos2θ          (iii)</p><p>Putting the value of sinθ in Eq. (ii), we get</p><p>     m2cosθcos4=n or cos3=m2n</p><p>∴   cosθ=(m2n)1/3 or cos2θ=(m2n)2/3          (iv)</p><p>From Eq. (iii), sinθ=mcos2θ=m(m2n)2/3=mm4/3n2/3=m1/3n2/3=(mn2)1/3</p><p>∴   sin2θ=(mn2)2/3          (v)</p><p>Adding Eqs. (iv) and (v), we get</p><p>     (m2n)2/3+(mn2)2/3=cos2θ+sin2θ</p><p>or   (m2n)2/3+(mn2)2/3=1</p><p></p><p>$